From a purely visual perspective, there's few things that are an immediate complete shutdown for me. It's more how the aesthetic is wielded to reinforce the game's themes that matters.
I would have to really go into a long explanation to fully capture what I'm trying to say, but since I don't have the time to do that right now, I will put it this way: I'm actually kinda okay with an aesthetic embellishing violence or sexuality unless the game is overtly trying to utilize that aesthetic to promote or celebrate mean-spirited and derogatory messaging. And to further complicate that, I can tolerate the use of mean-spirited and derogatory messaging within the context of a game if it is presented to the player as the challenge to overcome and the player is given adequate agency to explore and dismantle it, though there is a thin line of tact between being a power fantasy response or a tactfully handled philosophical challenge to the player — at the end of the day, the game is going to have to say something about whatever it's exploring (even if that something is "eh this is just for fun, don't sweat a thing") and the aesthetic is going to reinforce that.
Aesthetics matter in exploring themes, but upfront aesthetic is rarely an automatic and strong rejection outright for me. Sometimes presenting an art style I'm not necessarily subjectively fond of but exploring themes that I genuinely find intriguing ends up being a pleasantly subversive experience — eg, I'm not really into 2B's gothic erotica maid outfit when I look at it out of context, but damn I can't deny Nier Automata just would not land as hard if that design element wasn't a part of the existential crisis that game explores, that dissonance between the art I'm seeing and the gravity of the narrative is absolutely amusing to me.