Is Therianthropy appropriative? No. Next question.
Is the Therian aesthetic appropriative? Well...in some aspects, yeah. This is my own personal experience.
I am defining appropriation as the stealing of ideas, customs, and culture of a minority group (race, ethnicity, religion, etc) without equal exchange from a majority group, thus making whatever is stolen seen as good when done by the majority group but bad when done by the minority group. Vague language, I know, with "good" meaning things like "authentic", "ethnic", "exotic", "unique", "hippie", "boho", etc while "bad" meaning things like "dirty", "unkempt", "gangster", "low class", "disruptive", etc. A good example is dreadlocks, how someone like Kim Kardashian can wear dreads and it is seen as stylish but when a black girl wears dreads she is seen as unkempt and out of dress code.
I was introduced to the Therian community through Youtube, then sequentially the Therian Guide then Tumblr, from there I got onto Kinmunity then the Instagram Otherkin scene, then back to here. So, I've been around. I often see the Therian "aesthetic" divided into a few aesthetics that revolve around the earth, forests, beasts, and animals (especially wolves and ravens). The stereotypical wolf tail and the wolf fanart. One aesthetic I have seen and still sometimes do see is "Native". This is where I see the appropriation lines crossed; and, honestly, also the stereotypical and racist lines as well.
Now, what do I mean by Native American aesthetic? I mean dreamcatchers bought from white outlet stores, white sage from the New Age tourist trap, headdresses from Spirit Halloween, all things I've seen white and non-Native Therians wearing and using in the community to make themselves seem more "animalistic"; which is, well, kinda (read: very) racist. However, the first thing that really comes to mind is art like this:
Stereotypical and inaccurate photos of Native Americans which are oftentimes used by white or non-Native Therians to make themselves appear more "authentic" and, again, "animalistic" or in touch with the earth and stuff like that to make themselves look cooler. I think that is where the "Therians are appropriating Natives" misconception comes from, a small minority using Native stereotypes for their own aesthetic.