The following question has been edited in order not to be confused with another pre-existent question which has been linked below in the body of this question.
Many times it is read something inherent the worship of Vishnu in which then the answerer wants to point out that He is the Supreme God. Other times such is the case if we mention Shiva.
Overcoming the necessity to have the two hugest largest schools of Sanatan Dharma: Vaishnavites and Shaivites [other than Shakta and others] I was wondering if there is a Non-Sectarian area or branch or series of texts or comments of those, in which it is not the preference toward a Deva to speak, instead a more neutral and detached rational analysis conduced over the History [or for someone else Mythology] of these Gods.
While asking this I will clarify that I am going to start a mini-research by myself on this, which is contained itself [partially] on the body of this question.
Sources for this question: Vedas for Sri Suktam and Rudra Path and Narad Muni for Ravana's stotram Shiva Tandava.
Vaishnavism, Shaivism: the two biggest divisions of Sanatan Dharma. Yet Gods work all togheter in the Trimurti, each of them with their own "tasks", it is told. In some places I have heard that Shiva utters " Ram" to regard Vishnu and honour Him. Inside the Yoga Shiva Samhita, Shiva says that the yogi needs to call the name of Vishnu under certain stages of Sadhana.
Om Mahalakshmyai cha vidmahe. Vishnu patnyai cha dhimahi. Tanno Lakshmihi prachodayat
The consort - wife of Vishnu is honoured by Shiva and called by Him in many circumstances.
You can find the proof inside the Chamakam Anuvakas part of Rudra Path and inside Maa Lakshmi Sri Suktam also Shiva is mentioned even if not by the name of Shiva but by another name related to Him.
आदित्यवर्णे तपसोऽधिजातो वनस्पतिस्तव वृक्षोऽथ बिल्वः । तस्य फलानि तपसानुदन्तु मायान्तरायाश्च बाह्या अलक्ष्मीः ॥६॥ Aaditya-Varnne Tapaso[a-A]dhi-Jaato Vanaspatis-Tava Vrksso[ah-A]tha Bilvah | Tasya Phalaani Tapasaa-Nudantu Maaya-Antaraayaashca Baahyaa Alakssmiih ||6||
Meaning: 6.1: (Harih Om. O Jatavedo, Invoke for me that Lakshmi) Who is of the Colour of the Sun and Born of Tapas; the Tapas which is like a Huge Sacred Bilva Tree, (The Golden Colour of the Sun represents the Fire of Tapas.) 6.2: Let the Fruit of That Tree of Tapas Drive Away the Delusion and Ignorance Within and the Alakshmi (in the form of Evil, Distress and Poverty) Outside.
Bilwa Tree is a clear reference to something dear to Shiva [Bilwa Ashtakam is the proof of that].
One another here
कां सोस्मितां हिरण्यप्राकारामार्द्रां ज्वलन्तीं तृप्तां तर्पयन्तीम् । पद्मे स्थितां पद्मवर्णां तामिहोपह्वये श्रियम् ॥४॥ Kaam So-Smitaam Hirannya-Praakaaraam-Aardraam Jvalantiim Trptaam Tarpayantiim | Padme Sthitaam Padma-Varnnaam Taam-Iho[a-u]pahvaye Shriyam ||4||
Meaning: 4.1: (Harih Om. O Jatavedo, Invoke for me that Lakshmi) Who is Having a Beautiful Smile and Who is Enclosed by a Soft Golden Glow; Who is eternally Satisfied and Satisfies all those to whom She Reveals Herself, (Beautiful Smile represents the Trancendental Beauty of Sri Who is Enclosed by the Golden Glow of the Fire of Tapas.) 4.2: Who Abides in the Lotus and has the Colour of the Lotus; (O Jatavedo) Invoke that Lakshmi Here, Who is the Embodiment of Sri. (Lotus represents the Lotus of Kundalini.)
If Kundalini is mentioned, the Shakti is mentioned. The Shakti is in combination and fused with Mahadeva Shiva. Shiva Himself cannot stay without Her in the form of Parvati and also Maa Kali. Maa Lakshmi is the divine Shakti of Vishnu but at the same time Maha Maa Lakshmi is Shakti manifestation Herself, the Sattvic manifestation of that. ArdanarIshwara is The completement and full fusion of Shiva Shakti Mahadeva. AUM.
Again, in Rudra Path, in the Chamakam Anuvakas, we can read this:
CHAMAKAM SIXTH ANUVAKA
Agnishcha ma indrashcha me somashcha ma indrashcha me savitaa cha ma indrashcha me sarasvatii cha ma indrashcha me puushhaa cha ma indrashcha me brihaspatishcha ma indrashcha me mitrashcha ma indrashcha me varunashcha ma indrashcha me tvashhtaa cha ma indrashcha me dhaataa cha ma indrashcha me vishhnushcha ma indrashcha meashvinau cha ma indrashcha me marutashcha ma indrashcha me vishve cha me devaa indrashcha me prithivii cha ma indrashcha meantariiksham cha ma indrashcha me dyaushcha ma indrashcha me dishashcha ma indrashcha me muurdhaa cha ma indrashcha me prajaapatishcha ma indrashcha me
This Anuvaka is titled as ‘Arthendram’ because all Gods are clubbed with Indra and Indra is God of Gods and he gets a share of all sacrificial offerings along with every God. Thus a bigger share is offered to Indra, the Antaryami. Thus twenty five Gods are invoked along with Indra to grant us benevolence. Agni, Indra, Soma and Indra; Sivata and Indra; Saraswati and Indra; Pusa and Indra; Bruhaspati and Indra; Mitra and Indra; Varuna and Indra; Tvasta and Indra; Vishnu and Indra; The two Aswins and Indra; The Maruts and Indra; The Visve devas and Indra; the earth and Indra; the intervening space in between celestial earth and Indra; the four sides (Disas) and the space above Indra and prajapati and Indra.
Here Vishnu is mentioned. These anuvakas resemble in the form to Rig Vedic chants. Here both the attendants invoque the Gods and the Gods call each others. It seems both here and in Maa Lakshmi Sri Suktam and also in all of the Mandalas of the Rig Vedas, that there is a recipocal relation: Gods- Worshipper, Worshipper-Gods and is also the voice of the Devas or Gods present into these chants.
Finally the conclusive shlok of the Tandava Stotram mention Maa Lakshmi:
Puja vasanasamaye dashavaktragitam Yah shambhupujanaparam pathati pradoshhe Tasya sthiram rathagajendraturangayuktam Lakshmim sadaiva sumukhim pradadati shambhuh II15II
The last line citing Lakshmi Shambhuh. The encountering of Maa Lakshmi is granted by Shiva. The protection of Wealth is granted by Shambhuh Sada Shiva. So clearly this conclusive line of this shlok states. Conclusions:
Hence my questions are:
Why would the kapalini think that Shiva does not worship Vishnu?
Why some people, some Vaishnavites sects or sub-sects especially would think that Shiva Himself does not worship or honour Vishnu?
And more in general:
3.Dued to the existence in the Corpus of SD of either Vishnu Puranas and Shiva Puranas, many non attentive readers, try to find ways to impose wether is Shiva or Vishnu that Ultimate reality.
The thing is being complicated by the post-Vedantas and Advaita schools and the new era interpolated translations of many texts.
So nowadays it seems that to know Shiva, one must be Shaivite, to know Vishnu, one must be Vaishnavite.
And it seems that devotees and students are more involved to try to state that God is 1, rather than truly accept the Trimurti manifestation and considering the Immanence of That Ultimate Reality and the Genuine Good Pluralistic Monism of SD, it seems that if nowadays some Hindu do declare themselves polytheists, they would feel inadequate by some "competition" that they are doing with the Adharmic "religions".
The rationality of some scholar is needed, in order to have a zone in which the devotee can choose either to worship both and find true informations about Them.
I have already read this Q&A thread written by another user who states the opinion which follows: Why doesn't Shiva worship anybody where as Vishnu worships him in all his incarnations? Based on the Puranas
From there urged inside me the need for this very question
Sita Ram Ram Ram
Om Namah Shivaya
Footnote: Rudraprasna or Rudra Path has to be found into the Taiitiriya Samhita of Krishna Yajur Veda. Also this thing is very important to highlight, considering that Sri Krishna is the 8th aavatar of Naarayana Sri Vishnu.
To know more about Sri Suktam, you can read the Q&A of Keshav Srinivas which follow: What is the significance of Sri Suktam which is part of Rigveda?
Further links to this Q&A thread, you can also read my previous Q&A https://hinduism.stackexchange.com/a/44065/22667 about that same topic in which is cited how Maa Lakshmi, Vishnu and Shiva are intertwined and related each others.
Additional notes [to constantly be kept up to date]: https://hinduism.stackexchange.com/a/2575/22667
Mahabharata partially does answer to my question.
Here it is found the very right answer which is one other causative for my question which should not be closed.
This answer concludes that one should choose among the partial ways of Puranas, wether to trust Shiva or Vishnu.
I think that with many more researches we will find other answers.
Indeed, I find that other answers are too sectarians under the same Q&A over cited.
I wish to receive a non-sectarian answer, whenever this is possible.
Conclusive disclaimer: Since the censorship of the moderators or the admins want that we erase our questions, based on their points of views, which they do not negotiate, I am going to post this as an answer also. If someone will erase that without explaining me why, I will consider that this website promotes and incites Censorship in the wrong way, since my post promotes knowledge and Dharmic researches over the scriptures, I think there is no reason to force me to delete it.