How many beliefs concern propositions which aren't probabilistically correlated with each other, though?
Also, this seems to ignore the possibility of deriving one's values from one's beliefs.
Also, this seems to ignore the possibility that people cannot research everything themselves, and therefore have to trust others to get some of their beliefs, and that if they have reason to distrust someone who happens to be using a true belief, they can justifiably distrust true beliefs. Climate change is extremely convenient for the left to promote leftist policies, to the point where anyone on the right who doesn't know a lot of science would justifiably think "the people who believe in climate change are probably engaged in motivated reasoning".
this seems to ignore the possibility of deriving one's values from one's beliefs
The possibility (or something closely related) is raised in the section headed "Causes of agreement between political views and factual beliefs" -- it's option (b) in the list near the start of that section. But that option gets dismissed rather rapidly. (Too rapidly, I think.)
Here is a new paper of mine (12 pages) on suspicious agreement between belief and values. The idea is that if your empirical beliefs systematically support your values, then that is evidence that you arrived at those beliefs through a biased belief-forming process. This is especially so if those beliefs concern propositions which aren’t probabilistically correlated with each other, I argue.
I have previously written several LW posts on these kinds of arguments (here and here; see also mine and ClearerThinking’s political bias test) but here the analysis is more thorough. See also Thrasymachus' recent post on the same theme.