So, yeah, there is a conversation to be had here about how to handle this sort of thing in games, above and beyond how bad the video that sparked it was. (Which was, I want to be clear here: bad. Not gonna go back and read whatever I said in the wee hours last night, so gonna put that out. Bad arguments in bad faith to make a bad video.)
But beyond talking about how bad the bad video is, there is some meat to get into here. Especially in how it relates to MU*s.
In-person games have a lot of ways to handle content; I've got some fondness for "lines and veils" and "the X-card." "Lines and veils" gives people the chance to set up "lines," which are things they don't want to deal with at all in game (say, "no spiders" or "no sexual violence") and "veils" which are things that can happen in the fiction but they don't want to be 'on-screen' (so, for instance, someone could put "torture" behind a veil, and while there could be torture happening in the plot it wouldn't be a scene focus or get any graphic description. (The scorecard @Carma has there looks to be based on the same lines.) The X-card is something anyone can play to veto an element that was just brought up, we retcon it and move on. ("'From the pit, you see the leg of an enormous spider start to-' 'X-card.' '-an enormous snake start to emerge!'" "'I start to cut off the rude shopkeep's-' 'X-card, no you don't.'")
The thing is, these are a lot more workable in smaller sit-down games with friends. With MUs, where it is a good bit more ad-hoc and with a broader group (and, yeah, where you frankly can't have the same assumptions of good faith that you have in a smaller in-person game), it does get to be a thornier issue. Twice as much so when it comes to any game with horror elements, where violating social norms is kind of key to the whole experience. Anything trying to appeal to as wide of an audience as a given MU* can't really work with the same degree of "everyone gets veto power" as a smaller game with friends.
Setting a "rating" for the game is a good first step, although it does come with the issue that ratings are kinda bullshit. (Fun fact: Taxi Driver was given an NC-17 over the climactic violence scene, so Scorsese kept sending "recut" versions of the film to try to get it down to an R. Thing was, he didn't cut a goddamn thing, he just desensitized the NCAA by showing them the same ultraviolence over and over until they decided it was an R rating.)
Putting out some hard rules across the games is generally a good idea, I think. As well as respecting players who ask that topics or details be "veiled," more or less as outlined above; even if it's a bit much to ask that "violence against children" not be a thing in any aspect of the setting, it's perfectly reasonable for a player to ask that it not be given detailed description or focus. It doesn't need to just be "players," either; I know one of the GMs on a L&L game has said they won't have a scene where a horse explicitly dies. You can't have a world where the cavalry charge is the height of military technology but no horses are ever killed by violence, but it's perfectly acceptable to say that they don't want to GM a scene like that or give/be subjected to descriptions of it.
Give players a chance to bow out for content just the same as we have to accept that sometimes real life obligations take precedence over being available for pretendy funtime events that our characters should be present for. Be willing to gloss over detail rather than lurid prose about things that make people upset.
You can't reasonably have a game of a hundred, or even like twenty, people where everyone gets complete veto power over anything else that happens in-game (and while content in one TT group is basically only the business of that group, characters in a MU* interact outside the scope of a given PRP).
As far as people using bad faith to try to escape consequences to their character... I feel like the only thing to do here is work out with the player/s involved what the consequences are, at least in broad strokes, and move on. Maybe do one or more abstracted rolls to determine outcome without getting into detail. Real people and their feelings are more important than make-believe consistency, but a MU* is by definition something that has to have a certain degree of fictional 'reality' holding together, or everyone's play experience suffers.
Much more than a TT group, a MU* has to have some points where the fictional reality of the setting takes precedence over personal comfort, and the answer has to be "take it or leave it."