Eskimo covers more than just Innuit (and I have no problem calling them Innuit, not Eskimo) and I looked in to it and don’t see even any significant number of Innuit objecting to Eskimo.
Provide documentation for “that’s what they want to be called”.”
Who is “they”. A certain Innuit group? All or a certain percentage? Determined how? Etc...
No. You’re weaseling. We’re done.