Phyllis Schlafly is an odd comparison to make. She argued that women should stay in traditional roles and out of public life (while as you mention, not following her own advice), whereas JKR and other feminists take the exact opposite view. Not sure I see the relevance of your analogy here.

As for Bang Face last year, what happened is that security staff kicked a group of males out from the women's toilets. I agree that this isn't an ideal outcome, much better would have been if these men had respected that women's spaces are not for them, and stayed out in the first place. The fact that their removal was treated as some sort of scandal shows how far we've lost sight of the rights of women and girls to have single-sex provisions.