Power - conservative women don't have the power that men do in this culture. And, their attitudes are informed by internalized misogyny. They are channeling a social system that you and other men uphold in way more meaningful and impactful ways than they do, even if you are actual allies. Yes, women uphold patriarchy too, yes, women sometimes harm men. And the fact remains that overwhelmingly, it is men are killing and raping women, men are beating and harassing women, little girls start getting accosted on the street as 10 or 11 year olds and nobody does anything about it, women still have to fight for respect and equal pay for equal work (even though that is the law). The right to be traumatized by that and angry at a male-dominated culture that not only allows that to happen but tacitly approves of it does not exist in relationship to anything else. It fucking stands alone!
Stop deflecting. Do the work — the inner work, because the outer work alone is not enough.