Keep in mind that we are generally talking about the difference between 60/40 one way and 40/60 the other way. Or 2:1 in the most extreme (UT,OK,HI,VT) cases. That leaves a substantial base of people who agree and disagree with you to interact with. You can still find an vegan society in West Texas or a megachurch in San Francisco if you really want to.
But you forget that in a lot of states, like the south, political divisions fall along racial lines. if you're a white, educated liberal in a small town in the deep south most people who share your partisan loyalties will be black people who still probably don't have much in common with you. They're also more likely to be more religious and socially conservative than you.