Men are also way more open to casual/anonymous sex.

I'd guess part of this is, aside from personal preference, social stigma. It's no problem for a guy to get laid whenever and pretty much with whoever. But in most societies/cultures, a woman's reputation can be damaged or worse if words gets out she has casual hookups. Back when I was in high school (30 years ago), any girl found to not be a virgin at 15-16 was immediately labeled a whore and ridiculed constantly, even beaten up. The boys were revered for the same, though.

There are also more serious possible consequences for women. Potential pregnancy, potential assault from an unfamiliar partner, etc.