Native American is a silly term, rather like African-American, I think. It's a clumsy attempt to mollify people who are trying desperately to be "modern" and politically correct, which is their psychological problem, not mine. However, if it makes them happy to say Native American, that's okay with me. I can't see why it makes them unhappy if I say "Indian" or American Indian in the context of a conversation where it is plainly obvious that I do not mean people from India.

First Nations is another clumsy term, and could actually be a misleading one in some cases. The American Indians were and are a people of many nations, some of which have displaced others out of various areas of land in very ancient times...so who was really first?

Then you've got the Inuit.

What difference does it make what you call American Indians as long as the context makes it clear whom you are referring to, and it's not a deliberately insulting or pejorative term?

"Call me any name you like, I will never deny it" - Bob Dylan

"A rose by any other name would smell as sweet." - Shakespeare

Names are temporary labels, nothing more. When the fashion changes, so may the name. It doesn't matter.