I am talking about monotheism and polytheism. When we refer to bagavat Gita we can see that bagvan gives answer to this, he is the creator, preserver and destroyer.
It was Supreme Brahman (through Krishna) who said Bhagavad Gita to Arjuna. In Anugita Parva of Aswamedha Parva, Arjuna asked Krishna to repeat Bhagavadgita but Krishna said it was not possible to him again and says he was in Yoga (union) with Supreme Brahman at time of Gita recitation.
Vaisampayana said, "The son of Pritha (Arjuna), having recovered his own kingdom, joyously spent his time, without doing anything else, in the company of Krishna, his heart filled with delight, in that palace of celestial beauty. One day, those two listlessly proceeded to a particular part of the palace that looked, O king, like a veritable portion of Heaven. Themselves filled with delight, they were then surrounded by their relatives and attendents. Pandu's son, Arjuna, filled with joy in the company of Krishna, surveyed that delightful mansion, and then addressed his companion, saying, 'O--mighty-armed one, thy greatness became known to me upon the approach of the battle. O son of Devaki, thy form also, as the Lord of the universe, then became known to me! What thy holy self said unto me at that time, O Kesava, through affection, has all been forgotten by me, O chief of men, in consequence of the fickleness of my mind. Repeatedly, however, have I been curious on the subject of those truths. Thou again, O Madhava, wilt repair to Dwaraka soon.'
Vaisampayana continued, 'Thus addressed by him, Krishna of mighty energy, that foremost of speakers, embraced Phalguna and replied unto him as follows.
'Vasudeva said, 'I made thee listen to truths that are regarded as mysteries. I imparted to thee truths that are eternal. Verily, I discoursed to thee on Religion in its true form and on all the eternal regions. It is exceedingly disagreeable to me to learn that thou didst not, from folly, receive what I imparted. The recollection of all that I told thee on that occasion will not come to me now. Without doubt, O son of Pandu, thou art destitute of faith and thy understanding is not good. It is impossible for me, O Dhananjaya, to repeat, in detail, all that I said on that occasion. That Dharma (about which I discoursed to thee then) is more than sufficient for understanding Brahman. I cannot discourse on it again in detail. I discoursed to thee on Supreme Brahman, having concentrated myself in Yoga. I shalt now, however, recite to thee an old history upon the same topic. O foremost of all persons, observant of duty, listen to everything I now say, so that, with an understanding adapted to my teaching, thou mayst succeed in attaining to the highest end. O chastiser of foes, on one occasion, a Brahmana came to us from the regions of Heaven. Of irresistible energy, he came from the regions of the Grandsire. He was duly reverenced by us. Listen. O son of Pritha, without yielding to scruples of any kind, to what he, O chief of Bharata's race, said, in answer to our enquiries, agreeably to heavenly forms.'
As said in Tezz's answer, Vedas are given priority over all other scriptures in Hinduism. There are many statements in Vedas, which describe dieties such as Indra, Brahma, Rudra, Vishnu as Supreme Brahman. Different schools interpret these Vedic statements differently.
Shaivites consider that Supreme Brahman as Sada Shiva (or by other name depending on subsects), Vaishnavites consider that Supreme Brahman as Vishnu (or any higher form of Him depending on Subsects), Advaitins consider Supreme Brahman as Iswara or Saguna Brahman (wrt Maya) and so on.
There are many scriptures in Hinduism which are classified as Shruti, Smriti, Itihasa, Puranas etc...
And among all scriptures Shruti (Veda) has the highest authority and the ultimate Shabda-Pramana.
Bhagvad Gita is a text inside Mahabharata which is itself an Itihasa. So, Bhagvad Gita comes under Itihasa portion.
In the Vedas we find many statements which seem to be contradictory (in the surface) and these give rise to various views.
In the Vedas we find statements like 'Indra is all and everything', 'Rudra is all and everything', 'Vishnu is all and everything' etc.. etc... Some which I also discuss here.
Indra is the Truth (Aitreya Upanishad)
Prajapati was only here in the beginning. He wished 'May I exist.' (Shatapatha Brahmana 184.108.40.206)
'Eka Eva Rudro Na Dwitiyaya' Rudra is truly one without second (Yajurveda 1.8.6)
'Tad Visnor yat Paramam Padam' / 'Place of Vishnu is the highest' (RigVeda 1.22.21)
Indra says 'Know me only, no Karmas can touch you' (Kaushitki Brahmana Upanishad)
Aditi is all Gods. (RigVeda 10.89)
And there are many many such statements like this which seem to show that, that particular God is Ultimate.
These gives rise to various views like:
1) Some think that this type of praise by Vedas to many Gods is just an 'Arthavãda' ie. Mere glorification.
2) Some think that this praise is actually to the Antaryami of Gods who remains as self of self of these Gods too.
3) Some think that prayers are true as they are as every god is just form of Ultimate Supreme God.
.... and so on....
So, Bhagvad Gita can't settle these disputed/diverse views because they already come from the higher authority Vedas.
And on being specific to Bhagvad Gita also there are various views like:
1) View that it is Vishnu who is described in Bhagvad Gita:
From Bhagvad Gita we know that it is Krishna who is without birth and death and who is the Lord of all and the Purusha and as Krishna is an incarnation of Vishnu these all things actually applies to Vishnu. E.g: Sri Vaishnavism and major Vaishnava Sampradayas.
2) View that it is Krishna who is described in Bhagvad Gita:
In Bhagvad Gita Krishna speaks and it is Krishna who is Ultimate and even Vishnu is incarnation of Krishna. eg. Also in Gita Krishna says 'Vasudeva Sarvam Iti' "ie. Vasudeva is all and everything.' and hence Krishna is everything and even Vishnu is an incarnation of Krishna. Gaudiya Vaishnavas/ ISKCONS have this view.
3) View that it is Param Brahma who is speaking through mouth of Krishna in BhagVad Gita:
Actually it is Param Brahman who is speaking through the mouth of Krishna. For eg. Krishna in Ashwamedha Parva tells this about Bhagvad Gita:
Vasudeva said, ‘I made thee listen to truths that are regarded as mysteries. I imparted to thee truths that are eternal. Verily, I discoursed to thee on Religion in its true form and on all the eternal regions. It is exceedingly disagreeable to me to learn that thou didst not, from folly, receive what I imparted. The recollection of all that I told thee on that occasion will not come to me now. Without doubt, O son of Pandu, thou art destitute of faith and thy understanding is not good. It is impossible for me, O Dhananjaya, to repeat, in detail, all that I said on that occasion. That religion (about which I discoursed to thee then) is more than sufficient for understanding Brahma. I cannot discourse on it again in detail. I discoursed to thee on Supreme Brahma, having concentrated myself in Yoga.
So, it is Brahman who spoke Gita making Krishna as medium. People believe many things as Brahman like Self, Devi, Shiva, Vishnu, Avyakta etc.... So, Bhagvad Gita is describing these things.
4) View that Lord Shiva speaks through mouth of Krishna in Bhagvad Gita:
It is Lord Shiva who spoke through mouth of Krishna during Bhagvad Gita. It's because Lord Shiva is Brahman and also while showing Mahakala form in Bhagvad Gita, it is stated:
तस्मात्वमुत्तिष्ठ यशो लभस्व जित्वा शत्रून्भुङ् क्ष्व राज्यं समृद्धम् |
मयैवैते निहता: पूर्वमेव निमित्तमात्रं भव सव्यसाचिन् || 33|| (Bhagvad Gita 11.33)
Therefore, stand up and win glory. Conquer your enemies and enjoy an opulent kingdom. Verily, by Me and none other they have been already slain; you be a mere instrument, O Arjuna!
Now, this is Shiva who is speaking because Arjuna asks the same question to Vyasa in Mahabharata and Vyasa replies it is Shiva:
Arjuna asked: ‘O great Rishi, while I was engaged in slaying the foe in battle with showers of bright shafts, I continually beheld before me, proceeding in advance of my car, a person of blazing hue, as if endued with the effulgence of fire. Whithersoever he proceeded with his uplifted lance, all the hostile warriors were seen to break before him. Broken in reality by him, people regarded the foe to have been broken by me. Following in his wake, I only destroyed those, already destroyed by him. O holy one, tell me who was that foremost of persons, armed with lance, resembling the sun himself in energy, that was thus seen by me? He did not touch the earth with his feet, nor did he hurl his lance even once. In consequence of his energy, thousands of lances issued out of that one lance held by him’.”
“Vyasa said, ‘Thou hast, O Arjuna, seen Sankara, that First cause from which have sprung the Prajapatis, that puissant Being endued with great energy, he that is the embodiment of heaven, earth and sky, the Divine Lord, the protector of the universe, the great Master, the giver of boons, called also Isana. O, seek the protection of that boon, giving Deity, that lord of the universe”.
Also in Ishwara Gita Kurma Purana it is told that the knowledge passed by Ishwara (Shiva) there is same which is passed by Krishna to Arjuna:
नारायणोऽपि भगवान्देवकीतनयो हरिः।
अर्जुनाय स्वयं साक्षाद्दत्तवानिदमुत्तमम् ।। (Kurma Purana II.11)
Lord Narayana Hari, in the form of the son of Devaki himself transferred this knowledge of Yoga to Arjuna.
So, it is Shiva who is described in Bhagvad Gita.
5) View that Krishna spoke anything in Bhagvad Gita just to induce him to fight:
This is also another view. Some think that Bhagvad Gita is spoken only to induce Arjuna to fight thus it has no authority. For eg. Arulnandi Shivacharya in Shiva Jnana Siddhiyar states:
When Partha seated on the car saw the assembled hosts and all of them his kinsmen and he refused to slay them with his sharp arrows and reign as king after their death, the willy words uttered by Vishnu to introduce him to fight, you accept as your higher authority. Why don't you also accept the words of Buddha Avatar of Vishnu, propagated for the conquest of Tripura Asuras ?"
However this doesn't mean that all Shaivites do not consider Bhagvad Gita as authority. There are also some Shaivites like Abhinavgupta who have written commentary on Bhagvad Gita.
.... and so on there can be other views too.
Anyway the point is there are diverse interpretations and diverse scriptures thus giving rise to various beliefs. Regarding this Suta Samhita of Skandha Purana in Yajna Baibhava Khanda states:
अधिकारिविभेदेन नैकस्यैव सदा द्विजा ।
तर्कैरेते हि मार्गास्तु न हन्तव्या मनीषिभि ।।
यथा तोयप्रवाहाणां समुद्र: परमावधि ।
तथैव सर्व मार्गाणां साक्षान्निष्ठा महेश्वरः ।।
The wise say that each of these sastras is intended for a particular class according to the individual qualification, not all for one. These paths are not to be rudely handled by the learned subjecting them to rigorous unrelenting logic. As all streams ultimately empty themselves into the ocean, so all these paths ultimately lead to the Great Lord Himself.
And finally I want to close this answer with one verse from RigVeda:
They call him Indra, Mitra, Varuṇa, Agni, and he is heavenly nobly-winged Garutmān. To what is One, sages give many a title they call it Agni, Yama, Mātariśvan.(RigVeda 1.164.46)
When Krishna references Himself in the Gita, he is referring to the Supreme Brahman.
In The Gospel of Sri Ramakrishna, Ramakrishna Paramahamsa says (available here, Chapter 25 - http://www.belurmath.org/gospel/chapter25.htm):
The pundit and Mani Mallick became engaged in conversation. Mani was a member of the Brahmo Samaj. The pundit argued vehemently about the good and bad sides of the Samaj. Sri Ramakrishna was seated on the small couch and looked on, smiling. Presently he remarked: "This is the tamasic aspect of sattva, the attitude of a hero. This is necessary. One should not hold one's tongue at the sight of injustice and untruth. Suppose a bad woman wants to drag you from the path of righteousness. You must then assume the heroic attitude and say: 'What? You witch! You dare injure my spiritual life? I shall cut your body in two right now.' "
With a smile Sri Ramakrishna said to the pundit: "Mani Mallick has been following the tenets of the Brahmo Samaj a long time. You can't convert him to your views. Is it an easy thing to destroy old tendencies? Once there lived a very pious Hindu who always worshipped the Divine Mother and chanted Her name. When the Mussalmans conquered the country, they forced him embrace Islam. They said to him: 'You are now a Mussalman. Say "Allah". From now on you must repeat only the name of Allah.' With great difficulty he repeated the word 'Allah', but every now and then blurted out 'Jagadamba'. At that the Mussalmans were about to beat him. Thereupon he said to them: 'I beseech you! Please do not kill me. I have been trying my utmost to repeat the name of Allah, but our Jagadamba has filled me up to the throat. She pushes out your Allah.' (All laugh.)
(To the pundit) "Please don't say anything to Mani Mallick. You must know that there are different tastes. There are also different powers of digestion. God has made different religions and creeds to suit different aspirants. By no means all are fit for the Knowledge of Brahman. Therefore the worship of God with form has been provided.
"The mother brings home a fish for her children. She curries part of the fish, part she fries, and with another part she makes pilau. By no means all can digest the pilau. So she makes fish soup for those who have weak stomachs. Further, some want pickled or fried fish. There are different temperaments. There are differences in the capacity to comprehend."
"He is indeed a real man who has harmonized everything. Most people are one-sided. But I find that all opinions point to the One. All views-the Sakta, the Vaishnava, the Vedānta-have that One for their centre. He who is formless is, again, endowed with form. It is He who appears in different forms: The attributeless Brahman is my Father. God with attributes is my Mother. Whom shall I blame? Whom shall I praise? The two pans of the scales are equally heavy.'
"He who is described in the Vedas is also described in the Tantras and the Puranas. All of them speak about the one Satchidananda. The Nitya and the Lila are the two aspects of the one Reality. It is described in the Vedas as 'Om Satchidananda Brahman', in the Tantras as 'Om Satchidananda Śiva', the ever-pure Śiva, and in the Puranas as 'Om Satchidananda Krishna'. All the scriptures, the Vedas, the Puranas, and the Tantras, speak only of one Satchidananda. It is stated in the Vaishnava scripture that it is Krishna Himself who has become Kāli."
All are referring to Satchidananda.
The Vedas mention Lord Shiva as Bhagavan. And, there are no scriptures which has more authority than Vedas . So, there is no way one should stop praying to a Vedic deity who is described as Bhagavan in the Vedas. Similarly for other Vedic deities. Their worship is ordained in the Vedic scriptures so it should also be continued. Bhagavad Gita or any other scriptures for that matter don't have the authority to say otherwise.
प्रमुञ्च धन्वनस्त्वमुभयोरार्त्नियोर्ज्याम् ।
याश्च ते हस्त इषवः पराता भगवो वप ॥
भगवः- Bhagavan Parameswara! धन्वनः- of your bow, उभयोः आर्त्नियोः- (tied) in the two ends, ज्यां- the bowstring,
त्वं- you yourself, प्रमुञ्च- untie. ते- your, हस्ते- in the hand, याः- which, इषवः- arrows (are present), ताः च- them also, परावप- take away (from direct presence).
Bhagavan Parameswara! Please untie yourself the string tied at both ends of your bow. Please also hide from our vision the arrows that you have.
विकिरिद विलोहित नमस्ते अस्तु भगवः ।
यास्ते सहस्रँ हेतयोन्यमस्मन्निवपन्तु ताः ॥
विकिरिद- Destroyer of miseries like sin, disease, poverty etc., विलोहित- Of white complexion, भगवः- Possessor of six glories like wealth etc., ते- to you, नमः अस्तु- may prostration be. ते- Your, याः- which, सहस्रं हेतयः- thousands of weapons, ताः- those, अस्मत् अन्यं- our enemy (sin), निवपन्तु- may destroy.
सहस्राणि सहस्रधा बाहुवोस्तव हेतयः ।
तासामीशानो भगवः पराचीना मुखाकृधि ॥
भगव:- Bhagavan! तव- Your, बाहुवोः- in both hands, सहस्राणि-
thousands of, हेतयः- weapons, सहस्रधा- are in many shapes. ईशानः- All-powerful you, तासां- of those weapons, मुखा- ends, पराचीना-
not facing us, but turned away from us, कृधि- please do.
Mantras are from Sri Rudram Anuvaka 1 & 10.
Also, Bhagavad Gita was composed during the end of Dwapara Yuga. Many beleif systems already existed at that time (from the earlier yugas Krita, Treta). So, there is no way people will abandon their belief systems just because of Bhagavad Gita.
Moreover, Bhagavad Gita is not the only Gita. There are many others. All of them are composed by Vyasa who is the author Bhagavad Gita. And various such Gitas uphold various deities as supreme.
Hinduism is a Henotheist Monotheist religion and the hymns of the Rigveda, the oldest scripture of Hinduism, mention many deities, but praises them successively as the "one ultimate, supreme God", alternatively as "one supreme Goddess", thereby asserting that the essence of the deities was unitary (ekam), and the deities were nothing but pluralistic manifestations of the same concept of the divine (God).
Further, Geeta is a itihasa from Mahabharat, but Vedas are Shrutis and Vedas describe many Gods as a manifestation of same Brahman. This includes Brahma, Rudra, Indra, Agni, Vayu etc.,
"Ekam Sat Vipra Bahuta Vadanti" - Upanishads
Truth is one but sages call it by various names
A Self realised Guru will ask you this, "What do you mean by God?"
Will someone/thing will become god if large enough people worship them?
What are the criteria for divinity?
In fact, these criteria are given many times in many scriptures in various forms. The names and forms of gods may differ, but the criteria generally remains same.
If understood that essence, one will not have such a question.
I will not present any solution for your question as I feel myself unqualified. But reading Upanishads may be a good starting point.
But, I can say this one thing. Hinduism is more about realising God yourself, rather than believing in god.
Note: Submitting to god is different from belief in god
In our religion we don't take sides of gods and fight others. That defeats the purpose. (I'm not saying such things never happened in ancient times, but rather it isn't the Dharmic Way)
For a hindu hundreds of scriptures and thousands of rules are only secondary to a single direct experience of God.
While giving discourse to Arjuna, the mind of Sri Krishna was merged in the BRAHMAN and thus he had been speaking as a BRAHMAN itself.
Unless we understand this crucial aspect, every word of Sri Krishna is bound to create confusion, as to his declaration himself as GOD.
He never said that he is the incarnation of Vishnu .
सर्वधर्मान्परित्यज्य मामेकं शरणं व्रज।
अहं त्वा सर्वपापेभ्यो मोक्षयिष्यामि मा शुचः।।18.66।।
Abandoning all attributes, come to Me as your sole refuge; I shall rescue you from all sins; don't be sorrowful
येऽप्यन्यदेवता भक्ता यजन्ते श्रद्धयाऽन्विताः।
तेऽपि मामेव कौन्तेय यजन्त्यविधिपूर्वकम्।।9.23।।
Even those who, being devoted to other gods and endowed with faith, worship (them), they also, O son of Kunti, worship Me alone (though) following the wrong method.
He was referring to the TRUE method for the benefit of spiritual aspirants. He was indicating that a true spiritual aspirant should follow the method that will give realisation of the BRAHMAN.
There is only ONE God.
In Rig Veda, the Almighty God was described in different names like Indra, Agni, Vayu, Vishnu, etc, according to the form, the Almighty's power was perceived.
The allegorical stories of Indra's slaying of Vritra, etc, have deep SPIRITUAL meaning, but understood by later day generations in too literal ways. This resulted in evolving of ritualistic concepts like Yagna, sacrifices, etc, in Yajurvedic era.
This lead to converting allegorical stories of/epithets like Prajapati used in Rig Vedic era into deifying different Gods like Brahma, Indra, Vishnu, into fixed forms and stories like Varaha, attributing to Prajapati Brahma, etc, were woven.
The degradation of SPIRITUAL CONCEPTS of Rig Vedic era to deifying different Gods like Brahma, Indra, Vishnu, into fixed forms and other stories was discussed in the answer given below.
If we go through the Bhagavad Gita properly, we can understand that Sri Krishna said he is the Greatest among various groups, such as Vishnu among Adityas, Vajra among weapons, etc.
What Sri Krishna said was from the point of view of HIGHEST SPIRITUAL thinking. It needs a great amount of understanding to understand the words of Sri Krishna.