I would also say religious faith works in much the same way, i.e. you have to be open to it. Which is why I'm surprised you and Warbler, two vociferous atheists, are nevertheless open to believing in the supernatural.
I don't think religious faith does work the same way. It's much more doctrinal than it is enquiring, and is capable of being brainwashed. It's also enshrined (literally) in all facets of life, and designed by those who pedal it to contaminate open minded thinking. It builds monuments to itself, pens songs about itself which impressionable children are often forced into chanting, justifies wars in its names, and political leaders ask for its blessing. Religion doesn't encourage the doubter/ heretic either. In that regard its a world apart from any belief in the supernatural which often invites doubters in. Supernatural is much more inclined to explore critically, religion punishes those who dissent. Supernatural has a relationship with science, religion doesn't. Supernatural looks to science to assist it, religious nuts (for the most part) don't, because they're terrified that science can debunk the bedrock of their existance
There is a much, much, much bigger evidence to support the existance of supernatural phenonmena, that is to say, things which can be shown to the balance of probability, but which science can't explain. Science however not only requires the removal of all reasonable doubt, it also requires an explanation. So even if you turned up with a pristine photogtaph of Mr and Mrs Ghostie that is beyond reproach, science would never fully accept this until such time as it can provide an explanation. Even the "40 year wave" is in flux now that it has been proven that it exists and can rear out of a sea from nowhere. Science said it couldn't and that it was impossible according to the laws of physics until one did just that in the North Sea but happened to break on an oil rig with all sorts of monitoring equipment on it which proved otherwsie
Religion can't really point to much tangible other than a book and the accounts of smack heads eating mushrooms. When religion has been prepared to subject its evidence to science (the Turin shroud) it has collapsed. There are still tomes of stuff super natural that science can't get near to explaining
I'm not an aethist incidentally, more of an agnostic, but I'm thinking of converting to Islam in order to restore my sense of sanity