For the first, it can be women too. For misogyny it’s harder. But there is a trend currently to attract and radicalise women into conservatism too. The trad wives movement. I don’t remember the names but there are movement for spirituality and naturalism that are also linked to trad wives. That is also a slippery slope : first you hook them spirituality, and at the end you have JK Rowling who is an anti-trans activist.

Women and men are not in the same groups simply because conservatives are misogynistic so they like to separate men and women.

Overall it is a culture war lead by the far right.