I don't think they're against drag queens, they view gender as a phenomenon based solely on biological sex. This is why I'm confused. The conservatives would go one step further and say that social roles are also defined on gender/sex (for them they are the same thing), the cons would be against drag queens and nontraditional roles for women. In this way the gender criticalists are "classical liberals" because for them all activity is available for both men and women.

I can see why it seems like picking and choosing deconstructing gender but it is not. The claim of what women and female are is different from the claim of what women and females should be allowed to do.