I often think of religion in the context of weirdness. Especially when I get frustrated with religion, I tend to see God as the biggest paranormal claim out there, and the Abrahamic religions being as crazy as Scientology but made respectable by time and custom.
That, actually, might be a good reason to also go looking for atheist versions of weirdness. We’re all human, after all, and therefore we’re all incurably insane.
Individual examples are easy to find. One of my favorites is the Time Cube. The person in charge there seems seriously mentally ill, but it’s an entertaining enough example of off-the-deep-end paranoid weirdness. He also seems to be an atheist loony, given to exclamations such as “There is No God, only Godism.”
But further than that, I begin to run out of steam. Since nonbelief is on the social fringes, I guess I’m wondering about what must be the fringe of a fringe, so my opportunities to accidentally wonder into this species of weirdness must be limited.
There’s a Ph.D. thesis here for an enterprising social scientist or cultural studies person.