I suspect that Hazlit didn't quite digest the broader point I was trying to make about intersectionality. Both of the Obamas obviously face systemic racism, and, as you pointed out, Michelle Obama faces systemic misogyny in addition to that. Those realities, however, don't erase the privileges that President & Mrs. Obama enjoy in terms of income level, religion, celebrity status, age, lack of disability status, etc.
I often wonder what part of "multiple-things-can-be-true-at-the-same-time" people fail to understand...