I had a little chat recently with a glaciologist and he told me about a student who had come from a very religious family. The guy had to learn all about the formation of Earth, etc, and decided to give up geology because it would put him at odds with his family and friends and he decided that they were more important.
So, you could say he rationally decided to keep his irrational beliefs.
Isn't that just point #2 from above? He rationally decided that his friends and family, and the values he is a part of, are more important to him, then being in geology, and some deep truth that it would supposed show him. Maybe he just didn't care enough about _this_ truth, compared to being part of the world he is in.