I agree with your sentiment that it's awful. However, personal distaste isn't a good standard to use for what should be permissible. If you use personal distaste as a standard, then that means
everyone's personal distaste has to be considered. Suddenly people with different political opinions are allowed to silence each other, people who have done misdeeds are allowed to silence others working to expose them, and any kind of injustice or tragedy that might occur can't really be reported on for lack of making people uncomfortable.
Nobody likes to feel uncomfortable, and under most circumstances, I think that's something that should generally be respected. But when something unjust or tragic is taking place, making people uncomfortable can motivate them to act. Take a look at some of the footage of the aftermath of the atomic bomb droppings in Japan: it's horrifying, disturbing, and deeply saddening, but it's those exact feelings that have kept world leaders from using nuclear weapons since. Do any research on the Holocaust and you're likely to see a ton of disturbing images, but that's because disturbing things were being done; really understanding just how bad it was is part of what motivates people to make sure it never happens again.
If you use a less subjective standard like violence versus non-violence, you have many of the same problems. A lot of humanity's worst problems are violent ones and if you want people to actually care, you need to be able to convey just how bad it really is. Other standards have other problems. Want to try and make a determination based on intent? That's basically a guessing game and it's going to be colored by your personal opinions. Want to try and make a value-based determination? That's inherently subjective, plus oftentimes the value in something isn't realized until much later when viewed in a broader context. Any standard you can come up with that disallows things you don't like will end up disallowing things that are way more important to make sure are allowed. And the real kicker is realizing that a lot of the things you dislike may be important to allow as well, so that people can see that there are nasty people out there doing nasty things and to give them the opportunity to decide how they feel about that and potentially respond.
This is why free speech is so important. It's not because we should respect the right of a bunch of demented psychopaths to take pleasure in others' misfortune, but rather because the same principle that permits them to do that permits much more important things that may be similar in content but different in context and because it's important that we see that there are people out there who take joy in others' misfortune. It's also why the question of whether this is taking place on a private site is only relevant to the question of "is," not the question of "should." Free speech is something that
should be guaranteed whenever possible, even if it
is not. Reddit has no obligation to guarantee peoples' right to free expression on their platform (and indeed they don't), but it's something they
should do. Like it or not, it's the right thing to do, even if it sometimes means allowing crappy people to do crappy things.