The Men in the show are more physically and emotionally capable of the hand to hand violence needed to combat the zombies. Though Andrea is becoming a very good shot. Looks like she will be replacing Shane as the leader of the Ruthless Party.

As for democracy in The Walking Dead, before Rick decided to announce himself group dictator in the last show, I think he had democratic support, if not a formal election result. The deliberations over whether to off that captured fellow seemed fairly democratic as well - though not so much for the captured fellow.

But in an advanced technological society, women are equally capable of engaging in most but not all useful labor, and relegating them back to sitting at home polishing the silver is a waste of half your human capital. To that extent, rolling back feminism is a non starter for high living standards.