This is why I find the concept of brainwashing/deprogramming fascinating from an epistemic perspective; you're essentially substituting one set of axioms for another. And it's often hard to determine who occupies the epistemic higher ground, since all camps will claim to do so. For example, liberals think Fox News is brainwashing people, and conservatives think academics at liberal schools are brainwashing people. Sometimes the only thing you can use to figure out what's true is secondhand knowledge (via a network of cognitive authorities that you've chosen to trust) plus your own judgment, which itself has inevitably been influenced by some set of chosen axioms.

And often each system of beliefs has epistemic protection against debunking... for example, religious believers may view debunkers as agents of evil/Satan, while conspiracy theorists may view debunkers as agents working on behalf of the conspirators. In both cases, one has a "rational" reason to be skeptical of (or even outright disregard) any arguments that attempt to undermine one's axiomatic system.