I suspect that women aren’t dating conservative men

Well, there are plenty of conservative women too, so that can't tell the whole story, can it?

Looks like conservative men and liberal women are in similar boats, statistically:

In broad terms, there are only 0.6 single liberal young men for each single liberal young woman; likewise, only 0.5 single conservative young women exist for every conservative young man. Statistically, in other words, about half of these ideologically minded young singles face the prospect of failing to find a partner who shares their politics.

This implies the liberal men are dating the conservative women, lol.