If a game you might otherwise be interested in had an art style you really, really hated, would you skip the game?

No, because i throught about doing that with Zelda Windwaker and i am glad i never passed up that game.

King of Fighters XIII was my favourite fighting game from last-gen, but with KOF XIV they decided to ditch the classic 2D sprites and went with cheaper PS2-looking 3D graphics. I did eventually buy it but several years after release.

Can't say this is a definitive example of what you're looking for. I did hate that they wanted to change the art style, but I might've still bought it at release if it didn't just look plain garbage anyway.
I didn't like the change of art style in Xenoblade 2 either, but I still bought and played it at release. So for me at least, I guess it'd take a pretty extreme scenario to totally put me off a game.

Theoretically, yes. But, I've never seen an art style that I "really, really hated".

^ It's never happened to me yet, and furthermore to this I will add, I cannot even recall a game with an art style I've disliked.
So no.

If it's a game I might be interested in? Nope. There were two times that I almost did this and that was with Wind Waker and Xenoblade Chronicles. Both ended up being some of the most amazing games I've ever played. I can't make that mistake.

I'll pass on SMT V if Kaneko is not at the helm of the character design and the like.

I also try not to touch stuff with Suzuhito Yasuda art, because I believe his art is trash.

Those have been my only cases of that so far. Very, very few times I consider it. Other times it can take me some time to get used to it for me, like with DMC5 and Xenoblade 2, but I play them anyways.

Probably not on its own, but it's a factor. I really didn't like the art style for MvC Infinite. It didn't make me specifically not buy it, but it was a significant negative.

Everything modern with a 16 bit design is a no for me.

Not for the art style but the art itself could be very low effort.