Much of what people say has always been strange about politics. It doesn't seem to be rooted in fact so much as in wanting to dunk on someone.
I remember when Roe v Wade was being overthrown and people would talk about how this was how "Men try to control Women's bodies" or something like that. The reality around that time was that the gender differences were a few percentage points[0]. Since then a gender gap has widened[1] but notably among Republicans. Voters for the Democratic party barely differ on abortion attitudes based on gender.
0: http://pewresearch.org/religion/2022/05/06/americas-abortion...
1: https://www.pewresearch.org/politics/2026/03/12/do-abortion-...