In a different thread I called another poster’s boss a dick, and someone else called the boss an asshole, and she felt the need to point out that her boss was a woman. So I’d say there are male-typical insults. I was going to contrast ‘bitch’ with ‘bastard’, which are commonly used equivalents here in the UK, but I’m not sure it’s used much in America.
You’d insult a man by calling him weak, a loser or incel, or accusing him of living in his parents’ basement. Something of that kind.
But really, I just see ‘skanky’ as a pretty minor insult, so it’s weird seeing people making a big deal over it. To me, the overall hurtfulness of what was said is far more important than the exact words used, or whether one of them could have a sexist connotation.