I came across the information that on the individual level, this is called belief bias:

Belief bias is a cognitive bias in which someone's evaluation of the logical strength of an argument is biased by their belief in the truth or falsity of the conclusion. This effect has been demonstrated in psychological experiments, and is independent of reasoning ability.

(ETA: A search of LW and OB shows that we've never discussed this particular bias before, at least not by name.)