Interestingly, over the course of my many decades on this earth, I have never been sexually harassed and intimidated by a woman. And I've been around a crap ton of lesbians. The reason for these policies in a gym, and for generally having an issue with Random Man is this:
Random Man: Something random
Woman: Appeases
Random Man: Ooooooo she likes me, I shall press my advantage
Random Man: Something random
Woman: Ignores
Random Man: Fucking rude bitch what's your problem?
Random Man: Something random
Woman: Fuck off
Random Man: Cunt
Random Man: Something random
Woman: Fuck off
Random Man: I was only trying to be helpful, I'm a <drumroll> Nice Guy. You misandrist women, you hate Nice Guys, you like cunts. Maybe I'll be a cunt, do you like that? Fucking feminazis.
Random Man: Something random
Woman: Smiles and chats
Random Man: She likes me I'd better touch her
Woman: Please don't
Random Man: Fucking cock tease
There is no response which a nasty man won't find a way to exploit. And the actual nice guys (not Nice Guys) don't do any of this. I met DH as a random man in a bar. But he didn't tell me what to do, didn't try anything until it was REALLY obvious we liked each other, didn't do any of the above. I don't hate men but my experience of Random Man isn't good. And if there weren't quite so many of them, wouldn't that be better for the ACTUAL nice men we'd ACTUALLY like to talk to.