Refused to watch at all owing to animation style? No, haven't done that. OTOH, as some others have said, my overall interest in a show can definitely be affected if I dislike the visual style.
The most notable example is almost certainly Teen Titans; I'd have been far more interested in that series if its early episodes hadn't been so sharply tilted toward an anime look. I'll also admit to a guilty-pleasure interest in the Scooby Doo franchise -- but I consider the "new look" of the current Shaggy and Scooby Doo Get a Clue series a step backward, and that's contributed to my lack of interest in that series. (It isn't the only factor; I think the franchise also needs Fred, Velma, and Daphne to help ground it, and the various series that drop them have never worked well for me.)