While you can debate about whether the distinctions you made between Left vs liberal are accurate for all, I whole heartedly agree that there is a growing division among people of different political 'identities'. I wonder then how much this comes down to exactly that - identity politics - as opposed to actual values and beliefs.

When you talk about your experience with how people used to be, when they could disagree about politics and then enjoy a meal together, do you think they identified with their beliefs as much as people do today?

I see a great difference between, "Hi, my name is Thomas and I vote Democrat," versus, "Hi, my name is Thomas and I am a Democrat." Once you allow your political beliefs to become an integral part of your identity, the likelihood that you will seek compromise or change your views becomes drastically smaller. Changing your opinions in this case is to fundamentally change your identity, or at least having to admit that part of your identity is flawed: let's be real, how good are we really at acknowledging our flaws?

This effect is compounded then when you have a political culture which doesn't discuss politics, but projects it. You don't talk, you shout. You don't disagree, you decry one another for hatred and bigotry.

This does not describe everyone of course, but it could help explain why people cannot seem to set aside their differences!