Eskimo is used by Inuit in Alaska, they do not find it offensive but Inuit in Canada do. Kind of the same way Indigenous people in Canada don't like the term "Indian" yet those in America don't mind. I would never call myself an "Indian" since its a term based on mistaken identity.
I think if one group find Eskimo offensive I think it's worthy of asking why and listening.
Why alienate a certain section of society just because you don't agree or understand.