Related: Referring to American Indians as 'Native Americans', which is often seen as over-inclusive by American Indians themselves since it implies you're talking about Natives to the entire North and South America. While not the worst thing, when you are specifically talking about the native tribes the United States pushed out and forcibly moved to reservations, the term 'Indian' is codified in law[0] and is what the group themselves embraced as their identity so that, as a whole, they could bargain with the United States government to obtain compensation for the tragedies endured.
The problem seems to stem from 'American' being synonymous with the United States, when in a literal sense it means the entire North and South America continents. People will probably know what you mean with context but it can be confusing, so adding on 'Native American' just requires more explaining whenever you bring it up when not among peers.
This is a good point, but I'd also be interested in seeing the opinion of Americans with heritage from India, since using 'Indian' to refer to Native Americans might inconvenience them.
https://youtu.be/kh88fVP2FWQ
0: https://www.bia.gov/