Honestly, I tend to have a decent record of not watching shows that I'll end up disliking - perhaps because I rarely if ever go into shows blind - and if you dislike the protagonist, you're almost always going to dislike the show itself. That being said, Sasuke from Naruto was just... cringe (but this was my first anime ever, so cut me some slack XP) and Cautious Hero's Seiya was also kind of a tool. XD
ETA: That being said, I'd love to watch a show with a protagonist I *really* dislike, yet somehow *really* love watching the show. XD