The point is a man in drag will never look or sound like a real woman. Justice's mere presence will remind the faggots that they are living a lie, so of course real women will not be welcome.
Besides gay events like a drag debut are always about deviant sex, and again she would not be welcome.
If Justice wants to support her "friend" do so from a professional environment, like work. There is no reason to further the association into private life. It's best to limit any dealings with the insane outside of asylums.