I tend to connect folk with paganism, too, so preferably folk horror relies on beliefs that predate the invasion of Abrahamic religions.
This tension is definitely a huge theme in these films, but it can take on different forms. There's a lot where the superstitious church is the root of the evil (
Haxan, again, demonizing what is a rather benign rustic tradition), and those where the pagan traditions represent ancient evil (usually human sacrifice, etc.) It's interesting to see which films champion the one over the other, or which ones see these as competing corruptions. You mention
The VVitch, which seems to try to have it both ways, as a critique of religious fundamentalism and superstition, but still portraying the Witch as the realization of those superstitions.
From what I've recently seen, I'd recommend
Penda's Fen, which isn't a horror film so much as a drama of a young man wrestling with certain contradictions in his Christian faith. Mentioning paganism, the term "elemental" is used, and I think it's a worthwhile substitute for what is a diverse collection of local folk traditions. One thing that pagans have in common, and most of these films seem to have in common in reflecting, is the veneration of natural, elemental forces. One thing that strikes me about these films is that in many of them, the landscape is such a central feature. The films are green and grey, you can almost smell the mist and mildew and settled rain. The sympathetic magic which is at the heart of pagan beliefs is palpably represented by making these natural elements into living and consequential actors, as opposed to the austere and sterile environs of cleanly civilization. I think that the different attitudes of cleanliness and consecration are vital to what folk horror achieves.
Dark Waters is a rather Lovecraftian horror set in a monastery and has no folk elements at all.
Does it not? I was thinking that it was one of those "monastary built on a sacred pagan site" stories where a elite cult of nuns were preserving these pre-Christian traditions. I saw this one several years back, so I'll have to revisit, but I think the folk elements have something to do with the main amulet.