Don't get me started with all the "non-Hispanic white" and "Hispanic white" nonsense. That's something I've never managed to make sense out of.
I'm Basque from the Spanish Basque Country, so according to the American census I'd be "Hispanic white", but someone from the French Basque Country would be "Non-Hispanic White", despite both of us belonging to the same ethnicity (Basque). The only tangible difference is that in addition to Basque I speak Spanish and they speak French. Everything else is the same.
Another example would be the thousands of Argentineans and Uruguayans of Italian descent. They would be Hispanic/Latino whereas the Italian-Americans are simply white, when the only real difference is that the former speak Spanish and the latter don't. Nonsense.
It depends where. "Indio/a" (the Spanish equivalent of Indian) is usually considered to be pejorative and offensive to use when refering to the indigenous people of the Americas, and the indigenous themselves frequently find that term offensive, prefering the term indígena (indigenous) or simply the name of their actual ethnicity (Quechuan, Aymaran, Guarani, Mayan, etc.)