Don't some interpretations of neopagan magic have a bit of the same idea as the religion thing here? The idea is that there isn't assumed to be any supernatural woo involved, the magic rituals just exist as something that an observing human brain will really glom onto, and will end up doing stuff that it is able to but otherwise might not have done.

I think Eric S. Raymond and Alan Moore have written about magic from this outlook. Chaos magic with its concept of belief as a tool might also be relevant.