🟥 Vaishnava answer ahead!
Lord Hanumana being an incarnation of Lord Shiva is famous, but isn't universal! Scriptures talk of multiple source-deities of Hanuman, for example:
Skanda Purana 1.01.8.100:
“Naṇḍī, the son of Śilāda, who was a favourite follower of Śiva, incarnated as the great monkey Hanūmān for rendering assistance to Viṣṇu of unmeasured splendour.”
Shiva Purana 3.20.07:
“In due course Śiva was born of it in the form of a monkey named Hanūmat. He had great strength and exploit.”
Garuda Purana 13.16.68:
“When Lord Rama incarnated on Earth, Vayu was born as Hanuman for rendering assistance to Rama.”
Sri Madhvacharya has clearly explained multiple times that Lord Mukhyaprana’s first avatara is indeed Lord Hanumana, through scriptural authority. He states conclusively:
“He (Vayu) was directed by the God to take three incarnations. In the first incarnation He carried the orders of Sri Rama. In the second incarnation He destroyed Kauravas and their army. In the third incarnation, composing the works that describe the blissful God, He obtained the name Madhva.”
[Vishnu Tattva Nirnaya-90]
Other sects are free to belief whatever else they want. The reconciliation with the Shiva and Skanda Purana cannot be kalpabheda, since Hanumana isn't a post, but a characteristic of Vayu. So, to reconsile this, we need to dive deep into tattvavada.
Hanumana’s incarnation was taken by Sri Mukhyaprana only, Who has been called ‘Rudra’ in the Vedas. As:
"O Prana (Life-Force)! You are Indra (lord of power); by your brilliance, you are Rudra, the protector.
[Satprashnopanishad 2.06]
Sri Vamana Panditacharya, in his commentary, explains it as: rudrastho jagatparito rakṣitāsi— ‘Being in Rudra, You (Prana) are the protector on all sides’. Normally, the name ‘Rudra’ is derived from ‘roditi rudrah’, but contextually, when the epithet is assigned to Vayu, it becomes synonymous with protection and brilliance. That's why in some scriptures, Hanumana is said to be the avatara of Lord Shiva, when in reality, He is indeed the avatara of Lord Vayu. This is even accepted in Ramayana, this:
“I knower of Dharma! If you are worshipped, Marut (Vayu) gets worshipped. For that reason you are to be worshipped by me.”
[Ramayana 5.1.122]
Regarding His attribution with Lord Nandi, two theories crop up: one is based on Hanumana's attribution to Lord Shiva, another is the curse of Nandi upon Ravana.
Lord Hanumana, as an incarnation of Lord Shiva is accepted from various sources, primarily the Shaiva-Shakta shastras and a few regional resentions of the Ramayana. The latter must not be paid heed, because poetic freedom maybe attributed to those texts. The former is a little complex. The Shaiva-Shakta tantras are branded as Chala-shastrani in the Bharadwaja Samhita, and hence, are to be entirely disregarded by the Vaishnavas. Regarding Puranas, kalpabheda maybe attributed. In some kalpas, Hanuman is attributed with Shiva too. But again, avatara-hood mustn't be falsely meant, owing to theological constraints and differences in hierarchy. Hanumana, when attributed to Shiva, should be understood as ‘avesha’ of Him and not ‘avatara’. That is because if it is contended that Shiva is supreme, then He wouldn't do anything beyond His nature, that is appear to have ‘ananya bhakti’ or ‘paramekanti bhakti’ towards Sri Vishnu as Sri Raghava. Moreover, this contention would justify the words such as ‘rudrāṃśaḥ kapisattamaḥ’ (Shiva Purana 3.20.12), ‘shivamsa’ (Skanda Purana 5.02.79.06, Ananda Ramayana 8.16.19) and others. Shivamsa/Rudramsa means the portion or avasesha of Shiva and not avatara of Shiva. In Shiva Purana 3.06.34, Nandi is described as ‘tava putro bhaviṣyāmi nandī nāmnā tvayonijaḥ’. Thus, whenever in any scripture, Nandi will be called as the source of Hanumana, the implied meaning would be Shiva only.
Another explanation is gathered from Vishnu Dharmottara Purana, which narrates a story between Nandi and Ravana:
“Seeing that the movement of the Pushpaka vimana was obstructed there, the night-walker (Ravana) looked around and saw Nandi, possessing the form of a monkey, seated on the peak of the mountain. Upon seeing him (Nandi), Ravana burst into laughter; thereupon, Nandi cursed him."O Ten-necked Ravana! Lord Shiva Himself sports on this mountain. Since you have approached His presence in your aerial vehicle and mocked me, I shall therefore pronounce a curse upon you: ‘Fierce monkeys of immense valor, resembling my exact appearance, shall be born in your lineage of Pulastya to bring about your total destruction!"
[Vishnu Dharmottara Purana 1.222.5–8]
Following this explanation, the Shiva Purana 1.01.8.100 verse should be understood, to mean that the beast bearing resemblance with Nandi’s appearance was born to render assistance to Vishnu of unmeasured valour. This is understood.
Now to the question, “Why don't we see Vishnu serving Shiva or His forms?”.
Well a simple exploration in a few of the reputed Shaiva pages will end this question. But they surely won't provide the reason for Vishnu’s actions!
Padma Purana, Uttara Khanda 235.25: “O powerful Rudra, in every age in My different incarnations I too shall worship you to delude the demons.”
This has been explained in the Mahabharata Tatparya Nirnaya 2.133–134: “Lord Vishnu sometimes worships Shiva; Sometimes He worships Rishis; Sometimes He worships Devatas; Sometimes He worships humans; He bows to them and praises them; He asks boons from them; He establishes Lingas; He asks boons from Asuras; He, who is eternally the Supreme Lord, independent, infinitely capable, infinitely knowledgeable and above all beings, does so to cause illusion to (some) people”
So Vishnu's supreme nature is indeed established. Further:
Śiva, the consort of Umā spoke again to Viṣṇu, "Give me this boon, O God, so I become eminent among all beings. By incarnating on Earth, O Keśava, worship me and get boons from me, O God of gods. From this, I will become worship-worthy to all the gods.”
[Varāha Purāṇa 73.42-43]
So, whenever in any scripture, instances of Vishnu worshipping Shiva for boons or for maintaining His ‘narayana-hood’ appears, it should be duly remembered that they are there for the purpose of delusion of the demoniac or the fallen. Vaishnavas of purity and righteous approach, should duly interpret those portions in that light.
Sri Krishnarpanamastu 🪷