Sadly, I think this is more a cultural/societal issue than one of religious doctrine.
It's not the only reason, but a big reason anti-semitism has been around so long comes down to the burden of xenophobia. The Jewish people have historically been a nomadic people -- the Old Testament is a long history of our people wandering righteously, settling down, losing sight of our foundations, losing our homeland, and wandering righteously again. I'm not saying that's the modern Jewish message, or that the nomadic ideal informs all Jews. I'm certainly not qualified to speak for anyone's beliefs. But as an ethnic religion, we have an unfortunate combination of traits. We're a group of nomads that refuses to wholly assimilate to the surrounding culture.
I can understand both sides to an extent. Hadrian's journals include his confusion and frustration at the actions of his Jewish subjects. Why are they so mad about us reconstructing Jerusalem and sacrificing a pig to consecrate it? Pigs are sacred to Demeter! Do they even care about fertility?
If you're not facepalming now, you should be. But the issue is a dangerous diametric in our basic thought patterns. On the one hand, all people should be free to live as they like so long as they don't hurt anyone. The Jews had and have every right to live a life separate from the surrounding country. On the other hand, most people -- especially miseducated people -- distrust what they cannot understand. Our refusal to assimilate has a tendency to frustrate governments and confuse our neighbors. Add a healthy dose of fear and you have an explosive mixture. Look at the Romani for another example. They're some form of Christian, if I'm not mistaken, but they've been persecuted and discriminated against for centuries too.
I wish I knew how to solve the curse of xenophobia, but the human problem we all have with the "the stranger" is a deeply rooted disease.