but I think a man could be a good CEO of a rape crisis centre, and a woman a poor one
Up to a point, Lord Copper ...
Rape can only be perpetrated by a man as rape specifically involves a penis (at least in English law). I think that women's services, run by women, for women, are terrifically important in this area. Particularly given the very low rate of conviction - to the extent that basically, men know they can rape with impunity.
A man is far less likely to understand that - indeed, hardly likely to understand that - there is nothing at stake for them.
And this particular person has lied about their sex, and talks about keeping work "fun" (in a rape crisis centre???)