Hi, though I shared some Indigenous voices who prefer the term "American Indian", I don't mean to say that "Native American" is passé. Obviously the term has a wide currency presently. In fact, the American Indian Studies program I participated in at Montana State University back in the 2000s has since been renamed Native American Studies. Apologies if the examples I gave came across as polemic.The fact that the study of indigenous cultures is still called that in the US is in itself a problem.
The problem that some Indigenous folks have with the term "Native American" is that it sounds "unquestionably" like the hundreds of various indigenous nationalities are, and should be, just one generic flavor of the American civic national identity. Just another "hyphenated American," blended into the U.S. nation-state. A similar parallel would be to call Scots "North Britons" and Welsh "West Britons" (or to lump them together as "Minority Britons" or "Peripheral Britons"); or to call Kurds "Eastern Turks", or Tibetans "Southwestern Chinese," or Maori "Native New Zealanders." The term "Native American" has a "generic", "engineered" feel which Russell Means alludes to.
Whereas "American Indian" has a poignant ring of a "continent-spanning race." The term "American Indian" is still used by the National Congress of American Indians (the official representative body of the 632 Indian Nations within the U.S.), and also by the radical American Indian Movement (A.I.M.). The term "Indian Country" is in wide use, and is included in the title of one of the main indigenous newspapers Indian Country Today. And, though not widely known by the American populace, the term "Indian Nations" is officially the self-designated equivalent to the Canadian term "First Nations." When the (U.S.) National Congress of American Indians and the (Canadian) Assembly of First Nations made a joint "Declaration of Kinship" in 1999, these 1,265 nations referred to themselves collectively as "the Indigenous Peoples and Nations of North America."
Still, I'm not here to argue whether Native American or American Indian is the only "right" term. Because they both have their place, with some indigenous individuals preferring one or the other. "Indigenous American" or "Indigenous North American" or "First Peoples" are other options which I sometimes tap. And, like others have mentioned, the ideal is to refer to the specific nation.