To be honest.

For the most part

If it looks "awful" animation wise, I can watch and enjoy it if it has other qualities, like good humor, music, story, characters, etc.
I love animation and art, so I guess I can be a bit of a snob.

I can't get into watching Gravity Falls or Steven Universe because I find the art styles of both series so damn unappealing.

It doesn't matter that much to me. But when you get into some shows like Adventure Time, where it's so bad you can't tell what you're looking at, then I find it to be a problem.

I can't take some shows as seriously as they want to be taken if they have a childish art style but am open to art styles in general

If I really love the story, then I don't mind, but if the story is meh, then I can't really stand it.

I like a lot of styles

What scarletunicorn said. I like elegant 2D animation style of Disney Renessaince and early Dreamworks. Only movies I consider visually beautiful are amongst my favorites but it doesn't means gorgeous animation alone can make a movie my favorite: while all 2D Dreamworks movie are visually gorgeous, the only of them I love is The Prince of Egypt, I don't consider El Dorado and Sinbad unequivocally good movies.

I agree with scarletunicorn. Good animation really contributes to how much I like a show. High quality animation is an indicator of how much effort was put into making a good movie or TV show.