We are headed towards either a split (if we are fortunate) or Civil War 2.0 (if we are not). The differences are irreconcilable at this point.
Huge swaths of politics have becomes a moral issue, and one side quite literally thinks the other is evil. Democratic process work great when you're trying to allocate and prioritize resources to problems in a similar value system.
Democracy doesn't work well when you're literally voting on two entirely different views of moral/beneficial/good. It can't. It's just a winner and a loser.
Separation is really the only (inevitable) way out. If you really think there is a reasonable (mechanistic) way you could get the conservatives to take the liberals view, by all means share, but I don't believe it exists.