I agree with all of this. The original Wicker Man is one of the great English language horror films, full stop, and it is interesting to me as a Canadian who grew up with a lot of UK media on TV to read a bunch of Americans reacting to it for the first time.
I think a large part of what makes the original so horrifying is because it could be a true story. There is nothing about it I can recall that is not plausible, even for the time it was made. There is no real supernatural activity or reason to think that the sacrifice and the rituals actually do anything - it's just faith, but in an "old religion" whose pagan imagery are still all over the UK. The songs are probably all actual old pagan songs, or adapted from similar ones. Part of Woodward's horror, the more he learns about the village, is the realization that his faith is not enough in a world where no one cares about it or takes it for granted as the truth. Maybe one day we'll see a remake where a heroic Scientologist (I assume played by Tom Cruise, surviving on the "donated" organs of lesser members) visits a small town where everyone is still Baptist, and they nail him to a cross to try to bring their saviour back.
For those who enjoyed it and want more but in different media, I highly recommend the XTC album Apple Venus and its companion piece, Wasp Star, but especially Apple Venus.
I also highly recommend a two-issue story from the early days of the DC/Vertigo title Hellblazer, issues 25 and 26, in which John Constantine visits a northern town with much the same issues. Lovely art by V for Vendetta's David Lloyd, and one of the creepiest stories I can remember in comics.