Useful analysis, and fruitful comments. Here in New Zealand, as a distant mirror to the USA, this matter partly takes the form of the ambiguity of the term Kiwi, which codes for all New Zealander on one level but on another for the white-settler (Pākehā) New Zealander as compared to the quarter of the population that is made up of Māori and Pacific Islanders and always identified as such and not as Kiwis (not to mention people from Asia, etc)—that is, as opposed to the Pākehā who are seen as 'normal' and therefore Kiwi. Same old same old even on the other side of the world and it is good to be reminded of it: https://trc.org.nz/theme-1-p%C4%81keh%C4%81-norm.

Actually, come to think of it, it seems that the concept of white privilege covers two issues, one to do with really concrete socioeconomic forms of privilege and the often unacknowledged social networks that perpetuate it--ancestral land acquisition (or loss), the youthful crime that is not prosecuted to the hilt in a career-damaging way because you come from a 'good' background (or vice versa), etc etc--and the other the somewhat more chronic and general issue of not being accepted as 'normal' as a minority, which seems to be the original meaning in Peggy McIntosh's 1989 essay 'White Privilege: Unpacking the Invisible Knapsack' which introduced the term according to one or two other commenters. Maybe this dual meaning of white privilege is the source of some confusion and arguments at cross purpose.