Well, first, I don't see any practical way in which the United States *CAN* be divided into separate nations based on a red/blue binary. I believe the only way to avoid permanent civil war is that the rational and levelheaded voices in the room need to step in and say "Let's start from some basic principles on which we all can agree, and work outward from there..." -- Obviously, that's much easier said than done. I don't think anyone expects it to be easy. It would be nice if the mainstream media cared more about factual reporting rather than the sensationalism of perpetual division. Since the media won't be ceasing that exploitation anytime soon, it's incumbent upon people who value fairness and common sense to use their oversized platforms to drown out those who don't.
Regarding bathrooms and locker rooms: that may be how YOU feel, as a woman -- that you wouldn't have a problem with the male gaze if it was always guaranteed to be respectful and nonpredatory. But then there are women who will feel the opposite way from you -- they don't want to be seen undressed by men EVEN WHEN they value and respect the presence of those men in their lives. I can tell you, firsthand, you'll find a similar split amongst male mindsets (with the biggest difference being the lack of systemic threat from female predators; at least as far as physical safety comes into play when implementing gender-segregated spaces).
So, whose mindset wins?
I think you make a valid point about the toxic self-definitions of masculinity that have pervaded society for so long. But the vague reference to "starting from scratch" is, in fact, that -- vague. What would a "starter colonist" entail? How do you "eliminate memories of oppression" when it unavoidably carries over into each new generation? How do we shut out all of theocrats without creating a new authoritarianism in the process?
I'm someone who is very open to considering alternatives. But vague platitudes are not feasible alternatives.