This polarisation is only skin deep. Both sides agree on most things. They're democratic; they believe in the modern nation state; they assume the primacy of the state over religion; they believe in the state as a caretaker, don't believe that society can fulfill this role, and don't accept personal responsibility; they both lean towards, or fully accept, collectivism.
What divides them is the old, tired conflict between nationalism and internationalism, only seemingly a strict dichotomy. Both ideologies have the modern nation state as their premise. The left also drank far more of the kool aid than the right. The right is more moderate, in other words: Less collectivist, less egalitarian, more inclined to believe in personal responsibility. The latter shouldn't be overstated, however, as their concessions to personal responsibility often take the form of being exceptions to the rule that the state should take care of you. There is no strong movement on the right to abolish nationalized insurance, welfare or medical care.
A very strong conflict appears to be between the conservativism of the right and the destructive drive of the left, but the right is far from principled. They're not conservatives at all, really. Think of change as a racing fright train. The left wants to accelerate and then completely derail it. The right wants to decelerate it a little bit but they wouldn't hit the brakes or jump off. They want the world back that existed five to ten years ago, back when there weren't so many screeching harpyies in the universities and eight year olds didn't become drag queens. They don't think about ending the welfare state, the war on drugs, foreign intervention, the surveillance state, militarization, the income tax, and so on.