In poker and other complex, high-variance, incomplete-information games, bad players often think they're winning players. Politics is also a high-variance "game." And high polarization makes political outcomes even more volatile and “swingy.”

Political activists/operators will sometimes be overly results-oriented (also a problem in poker and other games): they may interpret a "win" for "their side" (whether an election or a swing in public sentiment on some issue) as evidence that they are taking the right approaches and saying the right things -- when actually it may just be a swing related to more people becoming sick of their opponents' antagonistic approaches and overreach (a common reaction in a highly polarized system).

This can lead to major mistakes in strategy: e.g., activists taking polarized, polarizing approaches who wrongly have been led to think "well, that worked, let's keep doing it" will later find out (or more likely, never realize) that those approaches are in turn what led to the same public never electing “their side,” or electing “their side” and then getting sick of them and unelecting them later.

Another factor here is that people on both "sides" can think "well, our opponents take highly aggressive, polarizing approaches and it works for them, so we should do it," failing to see that their opponents would be doing much better (not worse) if they didn't take those approaches. In all sorts of ways, our emotions lead us to see what we want to see; often we simply WANT to take highly antagonistic and contemptuous approaches (approaches that disregard and disrespect opponents' perspectives), and so we look for reasons to do that.

Also, survey results and their interpretations are known to frequently be very bad and misleading; but again, there, we often see what we want to see.