I've seen that many people do devotion in madhurya bhava (the emotion of lover-beloved) to male Gods e.g., Krishna, Shiva, Rama etc.
In a similar way, can a devotee have madhurya bhava towards goddesses such as Radha, Parvati, etc. or is it forbidden?
Now it is also said that tvameva sarvaṃ mama deva deva (you truly are my all, my god of gods)
How to make sense of this?
The purpose of devotional practices is to feel closer to one's deity or God. Closeness towards God will only increase if one thinks of God as a personal relative rather than the all powerful all knowing God. Hence, devotee saints suggest to practice devotion in the sentiments of a friend, parent, lover, etc. As the devotion towards God increases, the bhava or sentiments automatically appear or one can practice them as per his eligibility and liking:
Although devotional service is one, it becomes manifested in eleven forms of attachment: attachment to the Lord's glorious qualities, to His beauty, to worshipping Him, to remembering Him, to serving Him, to reciprocating with Him as a friend, to caring for Him as a parent, to dealing with Him as a lover, to surrendering one's whole self to Him, to being absorbed in thought of Him, and to experiencing separation from Him. This last is the supreme attachment. [NBS - 82]
Just like a person when falls in love always thinks about his/her beloved. So also a devotee who falls in love with God always remembers his deity. Hence, madhurya bhava or kanta bhava (the sentiment of a lover) is said to be the best among all types of devotion. Because, in it, a person feels more closer and attached to God. And the scripture says, irrespective of lust, love, anger or whatever, if one directs his feelings towards God then he attains Him:
Persons who constantly direct their lust, anger, fear, protective affection, feeling of oneness and friendship toward Lord Hari are sure to become absorbed in Him. [SB - 10.29.15]
However, unlike love between two persons where taints of personal desire may persist, in devotional practices love for God is clear and crystal like the rays of the Sun. There remains no personal desire but only the desire for the Lord's happiness. Madhurya bhava is the top most devotional sentiment which only a few, out of the many, practice properly. And for those few, God is truly their everything; starting with mother, father, friend, knowledge and wealth, to all other gods (twameva mata cha pita twameva....mama deva deva).
TL;DR No, this is inappropriate. However, according to the Vedas, you certainly can worship a deity/devatha of your choice. It must be noted that madhurya bhava is not something one can imitate. It is something that occurs naturally towards one's ishta devata when one is in advanced stages of devotion.
Below, I am going to present what the Vaishnava perspective (that I am familiar with) is describing the position of different gods in relation to the Supreme Atma. The Supreme Atma is identified to be Narayana, for He alone is the Paramatma of all living entities including the gods and goddesses and He alone has a śarīra-śarīri relationship with all living entities. For instance, the Subala Upanishad, as well as the Bruhadaranyaka Upanishad declare
yasyātmā śarīram. "He for whom the ātmā is the body" (Madhyandina recension of Brhadaranyaka Upanishad 3.7.22).
In other words, all jivāthmas (including various gods and goddesses) form the body of Paramāthma.
This idea is supported in the Ramayana, wherein we find Lord Brahma declaring to Lord Rama that the entire cosmos consisting of all sentient and non-sentient beings is His body:
jagat sarvam śarīram the (Ramayana 6.117.26)
and he mentions that he himself, his consort Saraswati, and the other gods created by him form His body:
aham te hṛdayaṁ rāma jihvā devī saraswatī deva romāṇi gātreṣu brahmaṇā nirmitāḥ prabho (6.117.24)
And in the Vishnu Purana:
tat sarvam vai hares tanuḥ
also supporting the same idea that everything is the body of Lord Hari
Now, further references from Bhagavad Gita
pitāham asya jagato mātā dhātā pitāmahaḥ vedyaṁ (9.17)
"Know Me to be the Father, Mother, the Supporter and the Grandfather of the entire cosmos"
gatir bhartā prabhuḥ sākṣī nivāsaḥ śaraṇaṁ suhṛt (9.18)
"I am the Goal, the Maintainer, the Master, the Witness, the Resting Place, the Refuge and the Best Friend"
Acharyas and Azhwars such as Kulasekhara have also talked about the nine types of relationship between the jivatma and the Paramatma. For instance, see this.
So, it is appropriate to develop such feelings only toward Him. For, it is said by Narada to Yudhistira,
"tasmād vairānubandhena nirvaireṇa bhayena vā snehāt kāmena vā yuñjyāt kathañcin nekṣate pṛthak" (7.1.26)
Manifesting such feelings toward other gods is artificial and improper for the following reasons:
"mamaivāṁśo jīva-loke jīva-bhūtaḥ sanātanaḥ" - Bhagavad Gita 15.7
"All jivas (including gods) are His amśas."
yathā taror mūla-niṣecanena tṛpyanti tat-skandha-bhujopaśākhāḥ prāṇopahārāc ca yathendriyāṇāṁ tathaiva sarvārhaṇam acyutejyā (Bhagavatam 4.31.14)
"Just as by watering the root of a tree, one satisfies its branches, twigs and leaves, and by supplying food to the stomach one satisfies all the senses of the body, similarly, by engaging in the service of the Supreme Lord one automatically satisfies all the gods and all other living entities."
The Antaryami Brahmana (3.7.2 to 3.7.23 or so) of the Brhadarnayaka Upanishad gives many statements of the type -
“yaṁ pṛthivyām tiṣtan prithivyāntaro yaṁ pṛthivī na vedā" "yasya pṛthivī śarīram yā pṛthivīm antaro yamayati sa ta ātmā antaryāmi amrtā”
which all essentially convey the idea that He, Narayana, exists as the inner controller of all these elements such as the sun, the earth, the eye, the fire, the water, the organs, the intellect etc.
And, all worships of gods go to Him alone (but that is indirect), as stated in:
"ye 'py anya-devatā-bhaktā yajante śraddhayānvitāḥ te 'pi mām eva kaunteya yajanty avidhi-pūrvakam" - 9.23 Bhagavad Gita
Whatever is requested of them by a candidate worshiping them, is only sanctioned ultimately by Narayana but through their agency.
"mayaiva vihitān hi tān" - Bhagavad Gita 7.22
"yānti deva-vratā devān" (Those who worship the gods go to the gods) - BG 9.25
but all such planets will get destroyed all the way until Brahma's at the time of total dissolution (maha-pralaya).
"ā-brahma-bhuvanāl lokāḥ punar āvartino 'rjuna.." (Bhagavad Gita 8.16)
Neither the gods themselves nor their abodes are therefore permanent and an intelligent person is not after temporary things.
"tasyaiva hetoḥ prayateta kovido na labhyate yad bhramatām upary adhaḥ" (Bhagavatam 1.5.18)
"kāmais tais tair hṛta-jñānāḥ prapadyante 'nya-devatāḥ" -
those whose intelligence is stolen by material desires of various types surrender to other gods (instead of Me, says Krishna) - (Bhagavad Gita - 7.20)
But the fruits given by them are also temporary:
"antavat tu phalaṁ teṣāṁ tad bhavaty alpa-medhasām devān deva-yajo yānti mad-bhaktā yānti mām api" (Bhagavad Gita 7.23)
"Men of small intelligence worship the gods, and their fruits are limited and temporary. Those who worship the gods go to the worlds of the gods, but My devotees reach My supreme planet."
One might then ask why worship of various gods and goddesses is mentioned in the Vedas. Because people of this world don't always desire the highest goal of liberation. They are more interested in temporary benefits of one kind or another. This squarely summarizes "conditioned existence". Because the Vedas are broad-minded and are said to have the compassion of a million mothers (Gita Bhashyam, Ramanujacharya, 2.46 purport), they sanction such approaches as mentioned in this verse of Bhagavad Gita:
"yāvān artha udapāne sarvataḥ samplutodake tāvān sarveṣu vedeṣu brāhmaṇasya vijānataḥ (2.46)"
"For a person who knows the self, all the Vedas are only of so much use as a flooded water reservoir is for a thirsty person."
(Purport by Ramanujacharya for this verse): All that is taught in the Vedas is not suitable to be practiced by everyone. A reservoir, which is completely overflowing with water is constructed for all kinds of purposes like irrigation etc. The thirsty person will only use enough to quench his thirst and not the entire content. Likewise, an enlightened aspirant seeking liberation will only take from the Vedas that which contributes directly to Liberation, and nothing else.
So one need not aspire for other benefits or forms of worship just because they exist.
The proper feeling toward other gods is one of reverence. One must respect them and offer due regards and obeisances to them, by all means. Daksha failed to offer proper regards to Lord Shiva and offended both Lord Shiva and Sati Devi, and got himself beheaded because of his attitude.
Even toward Narayana, feelings of madhurya bhava are artificial to manifest immediately unless one has advanced by leaps and bounds in devotional service in previous lives. Souls such as Mirabai, Godadevi, etc are exceptions. One should not imitate but begin with reverential devotional service which will naturally, in course of time, if properly applied, mature according to one's application in a particular way. This is what authoritative acharyas in all sampradayas have taught.
Putting it all together,
(Stage 1) one can go to the gods to fulfill one's material desires. That is okay, and allowed according to the Vedas. But manifesting madhurya bhava toward Radha or Lakshmi or Parvati is not appropriate. Ravana had so much lust that he was not satisfied after getting any number of good looking women. He went all the way to the Goddess of Fortune. He got himself destroyed. So, it might even be better to be an atheist and not have any faith in any form of God than lust after goddesses artificially. That is extremely injurious.
(Stage 2) If one recognizes Narayana as the Supreme Overlord of everything and directly go to Him for material desires, that is better.
(Stage 3) If one goes to Him only for liberation, giving up material desires altogether that is even better.
(Stage 4) If one goes to Him desiring Him alone and relationship with Him, that is the best.
If one is still attached to a particular god, but willing to move forward toward liberation, one can pray to that god to increase their devotion to Narayana. They would feel quite fulfilled by your desire and bless you with all their hearts to move forward. Vaishnava acharyas, in particular, have disallowed their followers from the adoration of other gods and goddesses because they did not want their followers to lose track of the goal of life, namely, liberation. But they never recommended disrespect of anyone. For instance, Madhvacharya says:
Pūjyā devās tataḥ sadā: "the gods are always to be offered respect"
People in the Sampradaya of Shankaracharya even worship all gods but with the understanding that they are, indeed, worshiping the Inner Soul within of all these gods.
Now regarding your specific question of Radha, Lakshmi or Parvati, Lakshmi or Radha are compassion potencies of the Lord and are often portrayed as mediatrices between the Lord and the jiva i.e., one takes shelter of Lakshmi/Radha to attain Narayana/Krishna. The way one takes shelter is, by considering them as a mother. If you've wronged against your father, you first try to go to your mother and then through your mother, reach the father. For example, Ramanujacharya prays in the Saranagati Gadya (verse 1):
"akhila jagan mātaram asman mātaram.. saraṇam aham prapadye." - O mother of the entire universe, my own mother, I surrender to thee (to reach the Supreme Father).
An acharya is, however, to be worshiped even greater than God because he is the one who gives access to God. He reconnects everyone to God. Therefore, we still worship Sankaracharya, Ramanujacharya, Madhvacharya, etc. But such sad-acharyas are also extremely rare.
I have presented what I have learned from acharyas. In my attempt to present this picture, I hope I have not offended anyone's feelings. My due apologies.
The answer I believe is no. If you have come to a point of liking Radha,I'm sure you probably have read a lot about her. Any person can realize that she literally breathes krishna,(not an exaggeration). It's always about seeing the happiness of your deities. I think it's more sensible to do what pleases her,I don't want you to be scared. They are your mother's and there are so many stories of people being cursed for liking goddesses in that way. Let's leave radha for madhav shall we.
