I've been reminded of talking to my dad about this last Christmas.
He was quite disturbed by the fact that an old friend of his (long time active Labour member, and Jewish) had left the party saying he didn't feel comfortable in it any more. The friend wasn't there to talk about it, and I don't know the friend that well, so I couldn't really talk about his position and motivations, but my dad was convinced that there was no anti-semitism on the left. I spent a while explaining that yeah there definitely was, I'd seen it, I could point to examples, this is how it works, blah blah, and maybe he took what I was saying seriously. But he just didn't see it on his own, and he apparently didn't generally encounter people who would explain the details to him rather than just be using it as leftie-bashing, and he would generally be defensive - "at the local meeting X was saying she'd never heard anything anti-semitic in Labour in her life, and she's Jewish" etc.
My dad is very ethical and sticks very strongly to his principles, and he is smart, but he isn't always necessarily that good on subtexts. I had to warn him about fringe stuff around some of the environmental/Occupy/etc movements that he was getting into a few years ago, not because the movements were bad but because I knew some of the types who hung around the edges and I knew he wouldn't notice it. Is he anti-semitic? I mean maybe by some definitions - he probably holds some unexamined prejudices and assumptions. But his response was mostly about defending an idea of the ethics of a group he felt part of because of their ethics, and he picked up on examples of clearly bad faith attacks to do this. He didn't blame Mossad or anything, he was just biased towards accepting explanations which wouldn't cause cognitive dissonance.
Of course, my dad isn't leader of the Labour party, so it doesn't really make a lot of difference to broader society what he thinks.
(NB I am not using this as a metaphor for anyone posting here. This is just me musing.)