"Joining" a party is part of the problem, not a solution.
I'm registered as GOP so I can vote in local elections which are almost always decided in the primaries. Realistically though, I'm much more independent since I don't have a lot in common with the religious right. While I will cross over and vote Democrat (I've never had to before) if a GOP candidate is anti-choice, I'll do that in the general election, so it's unlikely I'll change my affiliation.
Likewise, I can't see progressive men moving to the GOP, especially now that the GOP has taken a hard right into extremism. Yet, progressives are pretty extreme in their own way.
As far as the demonetization of males, that's not right, but it's probably going to get worse in light of the extremist anti-choice measures in some states. You're Jewish, so you understand abortion on a higher intellectual level than evangelical protestants do. They're more akin to the swine you're not supposed to cast your pearls before. What I'm trying to say is that the extremist abortion rules set in place by the evangelicals will deepen the rift between males and females and set males up as even bigger predators and enemies.
Our two-party system is failing us--we've outgrown it--but I don't see any viable alternative on the horizon.