A character can behave badly and still be accepted as a protagonist as long as they're likeable. (...) I would not want to read about an anti-semite, for example, no matter how good looking and charismatic they are. Ditto for an abuser of children or women. It is for this reason that every single AVENGERS writer since Shooter has had to play "damage control" on the character of Hank Pym after Shooter made him, in a lapse of his established characterization, strike his wife. And nobody (except the Japanese) has done a rapist hero.
I know what you mean and have often wondered about this. Does the protagonist always have to be likeable?
Surely it's okay to portray the the main character as a person with failings and moral lapses. In fact, the "hero" of Greek mythology is not necessarily someone who performs heroic feats by our modern standards (saving children from burning buildings and all that), but is a character who is larger than life. Achilles is a hero, for instance, but he behaves like a bloodthirsty maniac, and is not portrayed as a particularly nice chap at all. As I mentioned recently in another thread, the main characters of French pulp fiction aren't always likeable or even morally in the right, just interesting to read about. Hence, Fantomas does some pretty monstrous things, like putting acid in bottles of perfume, or unflinchingly sending an innocent man to the guillotine in his stead. I suppose Fu Manchu and Hannibal Lecter are also pretty good examples of this sort of character.
I remember being fuelled by an irrational hatred for Hawkeye in a miniseries back in the 80s, because he turned out to like Mantovani. I was recently turned off Marvel's The Ultimates, because of the anti-French stance the book, and especially its version of Captain America, adopted. I still bought it, though. Similarly, there might be things about Batman that I would really dislike if I knew them -- for all I know, Bruce Wayne believes in Intelligent Design and thinks global warming is bunk. (As an incurable old leftie, I'm happy to say that the Superman of Birthright is the sort of fellow I'd probably get along quite well with.)
In a way, this holds true for all our heroes, and sometimes one has to separate one quality from a thousand blemishes. I rather admire Winston Churchill, for instance, even though he was Conservative and I'm not (and he also said some very racist things in his day); I love Schubert's music, but I have no idea what his political views were and I don't really like the fact that he frequented prostitutes. Baudelaire and Shelley wrote some beautiful poetry, but I have no doubt that they were both unspeakably horrible men.