Imo this quote from her response is a pretty weak argument:

"The concept of female privilege is, AFAICT, looking at the disadvantages gender-non-conforming men face, noticing that women with similar traits don’t face those disadvantages, and concluding that this is because women are advantaged in society. "

In order for this to be a sensible counterpoint you would need to either say "gender conforming male privilege" or you would need to show that there are few men who mind conforming to gender roles. I don't really see why anyone believes most men are fine with living out standard gender norms and I certainly don't see how anyone has evidence for this.

If a high percentage fo men are gender non-conforming and such men are at a disdadvantage in society then the concept of male privilege is seriously weakened. And using it is dangerous as it might harm those men to here that they are "privileged" when this is not the case (at least in terms of gender, maybe they are rich etc).