Speaking for myself, I don’t think whether whomever it is says they have (or don’t have) such-and-such cultural ancestry is relevant. Neither left nor right.
Attacking Senator Warren for saying her family told her she is of Cherokee descent; or attacking Obama because his mother is white or his father is African. Or whatever.
It’s the deliberate distraction from more important issues, that is the goal of such accusations, that I have serious issues with. eg. “But her emails!”