TeaDidikai
Deoridhe
Yes, the appropriation of Buddha into Hinduism WOULD be a case of cultural appropriation which is inconsistent on both ends.
Is it appropriation or Vedic commentary on Shramana tradition in the same way that the verses within the Qu'ran are Islamic commentary on Christian tradition?
I think a lot would depend on whether you were Buddhist or Hindu, and within those how ...the word coming to mind is "strict" but perhaps "precise" is more accurate you are as a religious person.
Buddha specifically refused to comment on the existence or lack thereof of Gods as the Buddha. He also contradicted and critiqued the Caste system which many Hindus still operate under, in particular by offering up one Dharma which even an Untouchable could hold to and which would allow for single-lifetime enlightenment/samsara/release from mana/etc....
As an outsider to both traditions, I viewed the move to claim Buddha as a face of Vishnu - much as I adore Vishnu and I do - as a way of undercutting and undermining the deeply radical critique Buddhism's structure made on thousands of years of Hinduism.
i am sure there are many within Hinduism who hold this belief without meaning to undermine the Buddha's teachings, just as I am sure there are many Buddhists who don't mind or consider the distinctions a nitpick which is brought about by attachment to mana instead of the release of attachment, and thus below/beyond their attention, but viewing both traditions as I do with curiosity, interest, and non-attachment to them, that is how the move appears to me.