I became aware yesterday of this article by Adrienne K. at Native Appropriations (h/t Shakesville), and recommend you read it (these two earlier articles of hers she links to at the end are also well worth a look). She’s been writing about this since June 2015 so it’s probably negligent of me to only become aware of it now, but regardless.
I don’t think I’m really qualified to comment on how to respectfully handle writing about Native Americans in fictional milieu, so I don’t want to say much about it myself. She raises a lot of important issues I wouldn’t have thought of. My first thought was that it’s probably impossible to win, because the most likely alternative is to not include them at all and it’s probably better to acknowledge that indigenous peoples existed and mattered, but that’s an incredibly low bar to set and, as Adrienne points out, misrepresentation may well be equally problematic if not worse (e.g. let’s not forget what happened with Stephenie Meyer, and that now a lot of people only know about the Quileute tribe because of her bastardised werewolf mythology).
Likewise it’s not really fair to say “well, if you don’t want to be misrepresented, you’d better volunteer your time to explain everything to any author who decides they want to write about your culture”, that’s an undue burden to place on anybody… but what’s the alternative, encouraging them to do shoddy research and misrepresent you in problematic ways? Once again, marginalised people(s) just can’t win. I don’t know what the answer is.
But please don’t put too much stock in my whitesplaining of this, go read the original articles.
Quick edit to add: here’s another really good article on this, by Chris Lough at Tor.