[I]n principle at least someone could be rational in not reconsidering [irrational] beliefs even in the face of much troubling counter-evidence. I wonder how much that actually happens; most people think, or at least think they think, or at least say they think, that their religious and political opinions are important and consequential.

The other side of this would be people who hold beliefs they fear may be irrational but really do not want to think about it and convince themselves that it does not matter; they would probably act the same anyway.