"If you find yourself disagreeing with Republicans more frequently than with Democrats over factual issues, that appears to be a sign of confirmation bias."

Only to the extent that you think Republicans and Democrats are equally wrong. I don't see any rule demanding this.

Since all accurate maps are consistent with eachother, everyone with accurate political beliefs are going to be consistent, and you might as well use a new label for this regularity. It's fine to be a Y if the causality runs from X is true -> you believe X is true -> you're labeled "member of group Y".

Tests for "Group Y believes this-> I believe this" that can rule out the first causal path would be harder to come up with, especially since irrational group beliefs are chosen to be hard to prove (to the satisfaction of the group members).

The situation gets worse when you realize that "Group Y believes this-> I believe this" can be valid to the extent that you have evidence that Group Y gets other things right.