Believing that every shy man is a potential rapist or psychopath (and there are many women who hold attitudes like that) is a whole other level of paranoia far beyond feeling uncomfortable because there's someone of the opposite biological sex in the bathroom with you.
Also, many people would rush to defend the transgender person; the same is not true for shy men, who are judged and shamed by women for no reason other than being introverted and not approaching them in exactly the way they'd prefer.