What I try to do is make an effort to adopt all the disliked beliefs as temporarily true (it's pretty hard) and do my best to understand why the person believes that and what the good points, if anything, are. It helps if you can imagine that the disliked thing was actually written by someone you trust, so you can think: "Hm, well, it might be wrong, but maybe I'm the one who's wrong! And in any case, I should try to understand."
I was reading a review of Trust in God, or, The Riddle of Kyon. The reviewer went through step by step and listed problems with the fic. Some of them I agreed with, and others did not. What really stood out was in a comment agreeing with it: "reading that fic usually just evoked vague anger and other unpleasantness." Not unlike the vague feeling of anger and other unpleasantness I felt upon reading the review.
I don't consider myself someone whose opinion can be trusted on the quality of the original fic. In addition to being every bit as biased as any hater, although in the opposite direction, I have Asperger's syndrome, and I don't trust myself to notice such things as people acting out of character. However, because of this, I know my revulsion cannot be due to the quality of the review. I looked for it in hopes of weakening any bias I have. I think I can safely say that my revulsion will prevent that from happening.
So, any idea on what I can do? I've always thought haters should just stay away from what they hate. That would work fine if I just hated ponies or something, but I don't think it's such a good idea in cases where ideology is involved. And if nothing else, I don't want a vague feeling of anger and unpleasantness to ruin a perfectly good fanfic, like The Death of Haruhi Suzumia.