You are free to disagree with the thesis, of course.
The title of his piece is almost certainly a reference to "How the Irish Became White" [1], so presumably not so much. I'm with you on the broader point, though, that the hand-wringing about who is and isn't white is silly, and that if it serves as shorthand for racially privileged people, that's pretty much fine.
[1] http://www.amazon.com/Irish-Became-White-Routledge-Classics/....
[0] https://www.amazon.com/Irish-Became-White-Routledge-Classics...