I'm sure it's a difficult position as a parent, although I have no experience in that department.
That said, have you wondered why you find those things "horrifying"? I might be a bit concerned if it was rape porn, but besides that I am unconvinced that there'such harm to come from children seeing porn, either at an individual or social level.
As I've noted before, if a child is looking at porn, that means they have a desire for it, which I think is difficult for parents to come to terms with. I certainly wouldn't want porn foisted on children, but if they are seeking it out through their own volition, there really isn't much you can do about it; a parent's treatment of a child viewing porn probably has more potential for a negative outcome than the porn itself since it is ultimately blaming human beings for their innate instinct. As if there is something wrong with naked adults having consentual sex, or practicing paraphilias.
I discovered porn when I was 10 through AltaVista image search. Just type in a female name and presto! By this time, there wasn't a whole lot my parents could do because I was going to look at porn one way or another. As with violent video games, parents have no governance over what their kids have access to at their friends' houses. In that case, establishing trust with your children will go a lot further than making them fear something that they innately understand to be practically harmless.
By the way, parents could actually talk to their kids about sex and, yes, even porn. If you're a good parent, your words will likely have an impact even if your kids continue to get their hands on porn.