I admit, it's hard for me.
I'm an artist, and I absolutely adore appealing art design. I get turned off really easily if the art design isn't something I'm feeling, and it distracts from my enjoyment of what could otherwise be a great experience. This applies to games, cartoons, movies, tv, etc.
I've definitely stopped watching a show, or playing a game, because the art style/design was just really ugly to me, and I found it distracting.
Interesting exception to the rule currently is Immortals: Fenyx Rising. Not the biggest fan of the art style, but it's also not egregiously unappealing, so I'm still enjoying the game. There are aspects of the art design I like (in particular the environments, and some of the monster designs). The human designs are ho hum, but not altogether hideous. They look kind of like action figures, and like it's going for a Disney Infinity look, but falling short of that (I actually like how the Disney Infinity characters looked, actually).
It's the only one that comes to mind of a game where I wasn't all in on the art design, but still stuck with the game.
I couldn't get into Salt & Sanctuary, despite enjoying the gameplay, because I just didn't find the art design appealing. I really tried, because I met the designers at E3, and they were such cool, friendly people, that I wanted to give it a shot. I played it for a few hours when it released, but eventually just dropped it.
There's this other game that had a really cool premise (I think the character was in the spirit world and could possess people or something? i played it ages ago), but I really didn't like the art style at all, and dropped it too. I can totally appreciate a wide variety of art styles, and there are definitely countless art styles that I admire and adore, that are all wildly different from one another, but there are a handful that I don't dig. I'd probably say the amount of art styles I appreciate and adore outweigh the few I don't by a significant margin.
