If the victims are the gender without the privilege (as the woman in OP suggests) and the victims are the same group of people who are making individuals in the group feel bad for wearing the same dress twice (as OP suggests) then the victims, as a group, are at fault, it seems to me.

Is an individual woman who wants to wear a dress again at fault? No, but it ain't a male privilege issue. It's a culture among women issue.

The woman in OP seems to be going for "this is yet another way the patriarchy is keeping us down" or similar vibe, and although I usually agree with those sorts of assessments and think toxic masculinity is bad for everyone of any gender, this is definitely an own-goal by women.

Insert obi wan kenobi "you have done that yourself" meme here.

Edit: This also assumes I accept the premise put forth by the woman in OP. Based on things I hear (and don't hear) from my wife and other women in my life, I'm skeptical that the woman in OP is expressing a universal, or even nearly-universal, truth about whether women can wear an outfit twice.