I take greater issue with "whiteness" than with "white privilege," as far as phrasing goes.

To me, "white privilege" is intended to refer to a very specific dynamic in terms of obstacles faced by BIPOC communities.

On the other hand, "whiteness" is this sort of deceptively-ambiguous term that people can mold into whatever they want, out of convenience and/or pettiness and/or hostility and/or passive-aggressiveness. It's getting to the point where the term "whiteness" is at risk of becoming so malleable that it's essentially rendered meaningless.