The could be type correlation in the sense of how much you naturally empathize with fictional characters and how much you can accept violence as a reality of life, I guess. I'm afraid any conjecture would just be conjecture unless you were polling folks with verified type characteristics. You might as well ask which types enjoy violent video games and which types are really turned off by them.
I've always had a fascination with darker elements of human experience, and pain is just part of life experience. I know for me, darker things both disturb and interest me because they make me think... and also they up the stakes. I've having trouble putting it into words -- I don't like seeing bad things happen to people, and I empathize with people; but for some reason the "horrors" of human experience have some kind of gritty relevance to me maybe because they ARE so intense and because they shape us and motivate us in some direction. It is one type of crucible in which character, courage, and clarity is formed.
I remember when Alien came out, I was only 11 and of course couldn't go see it. But I bought the book adaptation from some school book fair, the cover said "on space no one can hear you scream," and my ISFJ mom took it from me and wouldn't let me read it. (Of course, that did not deter me.) The violence inherent in the movie is based on primal fears of being impregnated by The Other, or grabbed by the Thing in the Dark, etc. It's not just meant to be a gore fest per se.
I guess it's where violence served no purpose, it can then seem banal or even offensive to me. Oddly enough, one of the movies (and few movies) I remember feeling offended by was "Surf Nazis Must Die." To start with, I experienced it as a stupid/pointless movie which I wasn't enjoying, and then I ended up walking out of the room after one character randomly bit off part of another character's cheek for no real purpose. I just remember it really offending me, although the magnitude of the act compared to, let's say the opening of "Saving Private Ryan," wasn't very large; it just seemed banal and pointlessly cruel and stupid. I guess the point of the violence really matters to me, how it contributes to the story and what it is accomplishing. Some other people just seem to focus on identifying their own feelings with a victim, so the point of the violence is irrelevant.
(It seems silly but the kind of movie I can't deal with is actually where a character is publicly humiliated or embarrassed, especially by unfair accusations -- I actually have to pause the movie a few times to get through the scene.)
I've watched some pretty intense movies otherwise, but it's how it all fits into the whole. (I just watched Kill List this weekend, which I can't get out of my head in terms of trying to figure the movie out. But it does have an occasional extremely violent scene, which was meant to make the movie feel unpredictable and keep the viewer on edge... and that is the effect it caused.)
Meanwhile, I am not a fan of Friday the 13th and that ilk.