yeah, this is kind of a tough one, though... because people need to be able to talk about the hegemony of the group that identifies itself as white at the expense of the groups that are excluded from that identification. and always saying something like "the cartel that calls itself white, where some members aren't even consciously colluding" is kind of a clunker. esp for people who don't think/read about this stuff on their own, and who just think of "white" as a simple and natural ethnic delineation, to the degree that any ethnic delineation can be thought of as simple or natural =)
race, including "whiteness" is a scientific and biological fiction invented and accepted to maintain (and hide) a caste system. but through the assiduous maintenance of that lie, it has become a different sort of social reality. not using the term "white" makes it incredibly hard to talk with most people about the issue. but using the term "white" as most people (superficially) think of it also helps cement its pernicious effects.
pretty difficult jam our society has gotten into there.
"the people who call themselves white" is the best terminology approach i've seen to dealing with this, but even that is still quite clunky, and may still make the speaker sound like a hand-wringing liberal to anyone who's not already on board with the viewpoint that race is a pernicious and unscientific lie.