Returning to a functional republic does require restricting voting, but there's an easier sell than gender lines. Do a starship troopers style system, where only doing some kind of dangerous but necessary or useful civic service earns a vote, non-transferable. That would also eliminate goblinoid leftist men and the sociopath cabal types.

This isn't women that are the problem, it's that women have been made insecure by Leftists who have done everything in their power to atomize them, destroy their families, and make them insecure so they vote the correct way.