One of the more popular theories of meaning is the network theory of meaning, that individual words acquire meaning by the network of words and meanings they're embedded in. Thus the word cat doesn't acquire meaning directly, but from the associated 'net' of meanings surrounding it, words like animal, fur, mammal, aware, mobile, and so on. In the network theory of meaning, each meaning is supported by and supports other meanings in the network. There are no absolute meanings, all meaning is relative to all other meanings. There are no anchors.
One of the quirks of human psychology is that we're often not aware of our own biases. If our belief or disbelief isn't absolute, but relative to a network of other meanings which we're not cogniscent of, and others have their specific position embedded relative to another, different network, it can be puzzling how and what supports that others' belief or disbelief. It's like being a spider, poised on a web strung between two trees, and catching the sun glinting off another spider in between two other trees. If we don't see the web of the other spider, it looks like the other spider is literally floating in mid-air, unsupported by anything. Only when we become aware of our own invisible means of support do we realize there is no mysterious 'floating' to be explained, just a spider with a web that is like our own, but obviously different.
I'm not saying that there isn't cognitive dissonance and compartmentalization going on, but I would suggest that the way people of faith manage their beliefs is not all that different from the way any of you manage your beliefs. You're ignorant of how your own mind works to manage its beliefs, so you are ill-equipped to place the same mechanisms that you employ in another when you find someone whose views and biases are so different than your own. It may be less a case of them having a defect in how they function than it is that you have a defect in your understanding of how you (and others) function.