a number of people seemed confused when I tried to explain my inability to believe.

Maybe this is key to the problem, such that they are able to build such a strong mental block between those two aspects of the brain so that the concept of the conflict of belief is actively rejected.

them to really, truly believe without (apparent) cognitive dissonance.

The problem is that you can only be sure about the appearance of such. The cognitive dissonance just needs to be small enough so that it doesn't manifest in outward action.