The way I see it (no pun intended): If I can't stand the literal sight of the anime then why would I watch it?
Pun noticed. Playing the devil's advocate, does the story not matter then? Even if it's the most ingenious story ever written, if the art looks like it was drawn by a 4 year old, does that negate the value of the content? Or the reverse, a masterpiece in terms of art, but the worst story ever created?
I agree with KawaiiC... Take the first 5 Episodes of Guilty Crown, Zetman or Eden of the East. Both with a great storyline and artwork. Then compare that to an animation style like Hajime no Ippo (from what I have heard has a cool storyline and is popular, but the artwork is not for everyone), Deadman Wonderland (where the animation cut corners but had an interesting storyline). Or those that concentrate more on the art and then the storyline flops, then sometimes they concentrate too much on animation and then the storyline flops and then there is no guarantee that the animation is any good.
Whoever has lasted more than 5 minutes of Blassreiter I will congratulate you. In the end the art heightens the enjoyment of the anime, vise versa. For example the animation for Togainu No Chi looks nice, but the storyline and script is not for everyone.