They've had the burden of being wrongly labeled "Christ-killers" for centuries.
Jews today are no more responsible for Christ's death than I am. It's just a ridiculous, illogical position, but it's fuel for antisemites. As support for their hatred, they cling to and misapply a handful of biblical passages including perhaps the favorite of Jew-haters, the one that appears in Matthew 27:25. In response to Pilate's public hand-washing and comment that he was "innocent of this man's (Jesus's) blood; see to it yourselves," the crowd replied "His blood be on us and on our children." Because some idiots may have made that comment, this somehow (in the minds of antisemites) condemns all Jews for all generations. Insane.
The antisemites also conveniently forget (or don't know) the passage where Jesus utters from the cross, "Father forgive them, for they know not what they do." He forgave the Roman soldiers, the pharisees and anyone else who may have had a role in his death. In fact, forgiveness is a central tenet of Christianity, but many "Christian" antisemites find the "eye for an eye" approach, which Jesus explicitly rejected, much more convenient.
Finally, the most important belief in Christianity is the crucifixion and resurrection of Christ. It is the underpinning of the entire faith. Christ had to be put to death so that we might be saved. "He himself bore our sins in his body on the cross so that, free from sins, we might live for righteousness; by his wounds, you have been healed." 1 Peter 2: 24.
I'm not preaching here. I'm responding to your question with a theological analysis. Any person who identifies as Christian but hates Jews is full of shit and not a Christian.
I think there are other reasons why Jews are despised. They tend to be educated and successful. That's threatening to some people. Many others, I think, are envious.