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.”
I can also think of some small-scale organized atheist weirdness, though these invariably have a political emphasis. Some groups on the sectarian fringes of the political left, for example. Or some of the more impressionable fans of Ayn Rand, though that tends to be more commonly an adolescent phase, mercifully enough.
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.