My theory (and it really is no more than a theory) is that sexist conservative men tend to have more innate respect for the vitally important (and still usually female) roles of mother and manager of the home. Whether that's because of fond memories of nanny in the nursery or matron at school I don't know, and of course it too often tips into an assumption that a woman's role is still largely in the kitchen or as a SAHM. But the respect for those roles is there: they respect those spheres, and the millennia of female passed down expertise that's gone into them.
Whereas lefty men, for whatever reason, don't value or respect these things. I used to move in very lefty/queer circles (don't worry; I'm better now) in the early 00s when postmodernism and queer theory was really starting to make an impact in the UK and what always struck me was the sheer disrespect and even disgust for the role of mothers. (Plus also the transactionalisation of sex which I think lies at the route of the trans movement). I think a lot of the current generation of progressive elites also came up in those circles and that's why they hate terfs so much, cos a lot of terfs are mothers for extremely obvious reasons that we don't need to go into here.
I'm just thinking out loud as I type but this is kind of how I see it. And it needs to be fixed because otherwise we're gonna see more female Gen As going down the tradwife route, cos that's where they think they'll get the most respect for their femaleness.