I live in an area where there's a lot of Native Americans--specifically, though, not Navajo, but rather Choctaw, Cherokee, Seminole, Creek, etc.
This is a hard topic--it's....not just that it's J.K. Rowling. The use of stereotypes based on false or altered information is pretty prevalent in literature and cinema against Native Americans as a whole, particularly the issue about lumping them in together as a large group or cherrypicking their history. The frustrating thing about this is that Native American culture isn't an overarching homogeneous culture; practices and history differ from tribe to tribe. To see a writer as popular as Rowling do it is really bothersome because her works are targeted at a young audience, audiences known for being somewhat impressionable.
With a culture or religion with less of an oppressed history, factual information has been more easily disseminated. That's not the case here; these are cultures that still struggle to be heard more often than not, so the use of various tribes and traditions in this sort of fiction rubs a particularly raw emotional nerve for some.
Not all, but some. There are several Choctaws who probably wouldn't care about this where I live, but then again, the most prevalent tales about Skinwalkers, for example, come from Navajo tradition, so someone of Navajo descent would probably be angrier about this.
Had Rowling done more research and been more inclusive, it probably would have been a non-issue using fictionalized versions of, for example, Navajo traditions and history, because yes, that sort of thing is prevalent in fiction for many cultures, religions, and histories.