I agree with the PP who said it depends on the disposition of the child. There are many adults who dislike horror and therefore age is somewhat irrelevant in that being older hasn't made them less scared or affected by horror films.
I have loved horror films/scary films all my life; as a child I begged to watch them and once I was finally able to, there was no turning back - I loved them and have never once had a nightmare off the back of a film.
Some children will enjoy the genre and not be bothered. Others will hate it and have nightmares. I'm certainly not advocating letting a 10y/o watch SAW etc... but at the same time, I often see parents reference what they deem to be a "scary film" and I'm thinking "since when is that scary?" - there is a lot of subjectivity about what is or isn't a scary film.
The spiritual side you reference is YOUR thing - it's your perception of such films, but it doesn't make it fact. People having nightmares after watching a scary film is based on again, their disposition and how they internalise such material. It doesn't mean some spirit or demon has jumped out of the screen and is now doing something to the person. If that were the case I'd have a demon for a housemate watching the films with me and supplying the popcorn!
You, of course, have the right to believe what you want, but attempting to impose those beliefs on others - including your children - is no less damaging than a child watching a scary film - in fact, probably more so. At least with a film they can switch it off knowing it was fiction and return to playing a game or watching something lighter.
My view is, if a child has a genuine interest in scary films, then there is no harm in letting them explore that interest in a sensible way (ie. gradually, with supervision etc).