You are making an amazingly important point. If one accepts "all models are wrong, some are useful" then it fairly directly follows that cognitive dissonance is essential and irreducible and when one encounters it maybe examine one's models? Aka how and why one thinks and feels?
Zen shout-out: This is non-dualism in another guise, and a key Zen practice is to confront irreducible dissonance and batter yourself against it until you are forced to develop and internalize higher-order cognitive and emotional models that can represent contradictions and reason/feel over them to produce useful results.
This might not seem like a big difference but it is. The former creates arbitrary roadblocks: people refusing the vaccines no matter the incentives. It causes people to form junk "science" to justify why 2 + 2 actually equals 5. The latter allows people to compromise: I'm not intrinsically opposed to X, I'm just opposed because of Y, and if you can solve Y than I no longer care about X.
People need to accept cognitive dissonance more. And accepting cognitive dissonance means accepting that sometimes you're the dumb guy or the bad guy. But everyone is the dumb guy or bad guy at some point, whether or not they accept it. Accepting means that you can correct your mistakes and be the dumb/bad guy less often.
Unfortunately it's against human nature to accept cognitive dissonance: it literally causes stress. I don't even think I can fully accept cognitive dissonances. But I believe we can teach people how to resolve cognitive dissonance better, so that people can accept that they have flaws and make mistakes, without accepting that they're a failure.