I'm pretty sure there is no one culture that can lay claim to the concept of 'spirit animals' any more than can the Greeks to homosexuality or Jamaicans to matted hair.

'Blackface' and native American ceremonial head-dresses are one thing ... (although I am pretty certain that native American tribes weren't the first to wear feathers in their hair either) ... and I would, moreover, be wary of donning (for instance) Rastafarian colours and items of apparel myself, because neither am I Jamaican nor am I a follower of the philosophy/religion and it would be irreverent of me to do so.

'Spirit' animals, however, belong to no-one and anyone trying to dictate otherwise will be laughed to tears, if they do so within my vicinity. I recommend you dismiss any attempts with the contempt they deserve; such things are as old as the human race itself and the sanctimony of those complaining about cultural 'appropriation' of them no more nor less than an objection to 'cultural miscegenation' — bigots love to espouse the vilest of philosophies whilst claiming the moral high-ground by virtue of an accident of their birth (whether their claim be based upon a physical or cultural characteristic, a rose by any other name smells as sweet).

What next ... anyone with a Celtic design tattoo obliged to laser it off, only people of Irish descent allowed to celebrate St Patrick's Day and only the Scots allowed to drink whisky? The Welsh to disband their choirs because the Greeks invented the Chorus?

Demanding respect for traditions of cultural significance is perfectly reasonable. Appropriating all such traditions as sacrosanct to one’s own culture irrespective of their universality is not … it is hypocritical.