Unfortunately, I can't just go with the story in these films as I can when it comes to, for example, Harry Potter despite my not believing in magic, or Lord of the Rings despite my not believing in Orcs. So a whole genre is basically lost on me. Which is a shame as when I saw the original The Omen in 1976 (age 15) it scared the crap out of me very enjoyably. Can't really it enjoy it now.
The problem is the metaphysics. It's not that I can't take the story seriously because I am an atheist. I couldn't take it seriously even if I believed God was real.
First of all, if hell, the anti-Christ, various demons, etc. exist, then so does God and heaven. But if God and heaven exist, then:
1. Any injustice done in the film will be more than adequately compensated - the guy that dies horribly battling demons goes instantly to heaven, so we really should be whooping it up in celebration when his head is sliced off by Satanic Forces (The Omen). We should be delighted, not horrified. [POSTSCRIPT - after an exchange with Randal Rauser I see this was poorly expressed. I don't mean any suffering we see in the film doesn't matter 'cos it's compensated for later; rather, I mean that once you're dead, you are, as a demon-battling warrior, presumably going to heaven. So when the chaps' are head-sliced and impaled in The Omen (both very quick deaths, btw), that's not an awful thing, it's a good thing: I don't see why I am supposed to feel bad about it. Plus, any suffering in the film (though a Bad Thing) will be comparatively short-lived, after which you get eternity in Heaven which will be great!]
2. The God vs Satan imbalance in power is like Mike Tyson vs the weediest wimp ever, multiplied by infinity. God can, at any point, snuff out Satan - Baal, or whatever devil is causing the head-swivelling, green-vomit-inducing possession, say (The Exorcist). Which raises the question: so why doesn't he, then?
Why doesn't God stop this devil dragging some poor innocent child's soul to hell, for example? I guess one could appeal to God's mysterious ways (skeptical theism) at this point, and say that some greater good is thereby achieved by the damnation of an innocent kid (not withstanding skeptical theism). However, I doubt God's ways are likely to be quite that mysterious. Major plot flaw.
Note that it's not my external failure to suspend disbelief that's the problem here. The problem is internal to the plot: the plot could at least be logically coherent, even if it's fantasy.
However, I still wouldn't be able to make sense of this demonic stuff even if I did believe in it. Which is one reason I don't believe in it. My problem with such demonic plots is the same as my problem with a superpowers film that displays glaring inconsistencies - like Ant Man, in which the mass of super-shrunk objects varies wildly depending on what the director wants to happen (high mass retained when Ant Man punches someone full size or cracks a floor on landing on it, low mass when it's a military tank you can conveniently place in your pocket). Once you've spotted the flaw, it really starts to grate, and enjoyment of the film suffers.
Well, for me, at least.