I feel the need to elaborate on my opinion a little, so here goes.
The only way I might be alright with a "hate" club is if the discussions were such that they were critical and thoughtful of why a character was either ill-conceived, poorly presented, or just didn't function well in the story. Unfortunately, I just don't see that happening. And besides, you don't really need a club for that. Feel free to start a thread for it in the FF sections if you think you have a strong case and put your venting to good use. What MOG referenced is case in point.
On the other hand, I do see the point where the love or pro clubs have a lot of nonsense associated with them. Hate clubs would also serve the same purpose of giving members a way to discover things in common with one another. The difference, though, is that a mutual hate for a character is a pretty shitty thing to have in common with someone, if only because there are more positive associations we could be making with one another.
Let's say I wanted to start a hate club for the color red, but I'm a huge fan of blue and green. Yeah, it would be nice to meet other people who also hate red, but I think I would be better served if I could just meet other fans in pro-blue and pro-green clubs instead. That's more positive, and to me it makes more sense to encourage that.
BTW I'm starting a hate club for hate clubs. Who's with me?