Absolutely there are horrible women; the difference is, no matter how horrible a woman is, she can't expose her penis to women and girls in a changing room, or rape another woman, or use her male body to win women's sports competitions.
I, along with millions of others, think third spaces are an excellent solution to many of these problems. Unfortunately, TRAs do not agree, deeming the very suggestion to be 'transphobic', as it violates the 'trans women are women, trans men are men' rhetoric.
Incidentally, transwomen are entitled to compete in sports in the men's categories, PROVIDED they qualify. They are not banned from competing in sports, as so many of them claim. By that reasoning, I am banned from all of the women's teams in all sports, as I am not good enough to qualify.