"The idea that people must give up these aspects of culture in order to be American, to blend into the larger country, is being seen as not necessary," said Jose Barreiro, a Cuban Indian and editor of the Akwe:kon Press, an indigenous journal published by Cornell University in New York state.
"People can retain their cultural identity and yet be part of American life," he said.
In contrast to Mexica and other indigenous groups, some people feel just as strongly about keeping "Latino" as an ethnic term of inclusion for people of Latin American descent.
Alan Clayton of the Los Angeles City/County Latino Redistricting Coalition opposes identifying people of Latin American descent as anything but Latino.
"It hurts the community politically," he said. "Then you'll have people who say you shouldn't count as Latino because you marked yourself as something different on the census."