In my own interactions I’ve found the hardened categories of liberal and conservative, or left and right, to be confusing and not helpful. Too many claim these labels without knowing what they mean.
I’ve never had difficulties interacting, even debating, with liberals in the best sense of that word, or conservatives in the best sense of that word. I have had much difficulty with illiberals who think they are liberals, and conspiratorial folks who claim conservatism. Neither are very knowledgeable of political philosophy or history.