How do we talk politics with someone who hasn't stopped to think about this sort of thing?

Or, more importantly, under what conditions is it optimal for one to "talk politics with someone who hasn't stopped to think about this sort of thing"?

So how can we successfully talk and reason about politics? What precautions should we take? How do we talk politics with someone who hasn't stopped to think about this sort of thing?

Well, it depends on what your goals are. But, generally speaking, making effective political decisions is very difficult and requires a specialized cognitive toolkit: the standard virtues of rationality do not suffice. There is a well-established literature on what effective political engagement might look like, and what cognitive tools might support this. Bernard Crick's In defense of politics is a standard reference.

Following Karl Popper: democracy is voting the wrong person out, not the right person in. And it is voting, not inheriting the role and not being beheaded to end a rule. This makes (Popper-style) democracy very much a less-wrong school of thought.