How about when one does not hold one belief to be prominently truer than another, but holds on to one consistent set of beliefs that their view of the universe and their morality are based upon, and which they cannot change gradually, because that would lead to inconsistency, and then one goes and accumulates enough evidence against the individual beliefs of one set and in favour of those of another set to decide to change sets entirely.
Religion-coded and other similar worldviews are not buffets, you either take the whole menu or nothing at all. You can't divide it in bits the same way you would treat, for example, Marxism. It's all or nothing.
To break up the awkward silence at the start of a recent Overcoming Bias meetup, I asked everyone present to tell their rationalist origin story - a key event or fact that played a role in their first beginning to aspire to rationality. This worked surprisingly well (and I would recommend it for future meetups).
I think I've already told enough of my own origin story on Overcoming Bias: how I was digging in my parents' yard as a kid and found a tarnished silver amulet inscribed with Bayes's Theorem, and how I wore it to bed that night and dreamed of a woman in white, holding an ancient leather-bound book called Judgment Under Uncertainty: Heuristics and Biases (eds. D. Kahneman, P. Slovic, and A. Tversky, 1982)... but there's no need to go into that again.
So, seriously... how did you originally go down that road?
Added: For some odd reason, many of the commenters here seem to have had a single experience in common - namely, at some point, encountering Overcoming Bias... But I'm especially interested in what it takes to get the transition started - crossing the first divide. This would be very valuable knowledge if it can be generalized. If that did happen at OB, please try to specify what was the crucial "Aha!" insight (down to the specific post if possible).