One workaround would be to assign high confidence only to beliefs for which you have read n academic papers on the subject.
Academic papers are what get's published, not what's true. The difference is particularly pronounced for political topics.
you should be able to accurately restate your opponent’s position
There are limits. You can't accurately restate gibberish. You can mimic it as in a Turing test, but I don't see any criteria for accuracy.
I think the best you can do is identify the unstated assumptions. When you can get both sides to say "If A,B,C the side1 is right, and if A~,B~,C~ then side2 is right, and if neither, then side1 and side2 each only has a piece of the truth."
You can't accurately restate gibberish.
Good point. If someone appears to be emitting gibberish on a subject, but seems to be a reasonably functional member of society (i.e. is probably not floridly psychotic), and there's nothing about the structure of the subject that seems to license gibberish (e.g. a subject where dreams or psychedelic visions are treated as unquoted evidence) this may indicate that you simply don't understand that subject and should learn more before attempting to judge their statements.
For instance, I would expect that a person who had no higher math would consider correct statements in category theory to be indistinguishable from gibberish.
So you're playing the credence game, and you’re getting a pretty good sense of which level of confidence to assign to your beliefs. Later, when you’re discussing politics, you wonder how you can calibrate your political beliefs as well (beliefs of the form "policy X will result in outcome Y"). Here there's no easy way to assess whether a belief is true or false, in contrast to the trivia questions in the credence game. Moreover, it’s very easy to become mindkilled by politics. What do you do?
In the credence game, you get direct feedback that allows you to learn about your internal proxies for credence, i.e., emotional and heuristic cues about how much to trust yourself. With political beliefs, however, there is no such feedback. One workaround would be to assign high confidence only to beliefs for which you have read n academic papers on the subject. For example, only assign 90% confidence if you've read ten academic papers.
To account for mindkilling, use a second criterion: assign high confidence only to beliefs for which you are ideologically Turing-capable (i.e., able to pass an ideological Turing test). As a proxy for an actual ideological Turing test, you should be able to accurately restate your opponent’s position, or be able to state the strongest counterargument to your position.
In sum, to calibrate your political beliefs, only assign high confidence to beliefs which satisfy extremely demanding epistemic standards.