Here's what one person (Janos Honkonen) commented in that discussion, which I thought was a pretty awesome description:

Okay, hmm. Imagine a situation where you started seeing a new color. It would be damn difficult to describe how it looks and why the heck you feel that seeing that color made things shine just a bit brighter and more beautiful, and somehow that gave you certain kind of serenity that somehow makes you be a bit less if a dick you'd probably be without it, maybe. Some other people would see that color and make a huge amount of noise and nuisance about it, and others would say that people seeing that color are deluded, idiots or psychotic. You'd sit in the middle wishing everybody would just shut the fuck up, especially those people who forget that the main "use" of the color is to see it and see a different world and you, not to make noise about it existing and harass other people about it.

This is more or less how it works in my head, and it's not like I can fucking help it. Instead of dimming it, learning about biology, the cosmos, neurology and psychology makes that color just burn brighter and more beautiful.

Also, Googling a bit I found this summary of Jonathan Haidt's research to the experiences of sacredness. Reading that and Janos' description together made me a little more convinced that actually, just about everyone has experienced something akin to religious belief - it's just that (some varieties of) religious people experience something similar far more often.

ETA: Janos pointed out that the experience of awe in nature and the experience of the divine feel different, and I should clarify that I didn't think that the experience of nature and the experience of the sacred would be exactly the same, just... somewhere in the same rough neighborhood of experience-space, analogous to the way that listening to a good song is quite different from reading a good book, but still closer to reading a good book than getting punched in the face.