Christianity is modified (Christians say "fulfilled") Judaism. All of the original Christians were Jews, and Paul, the person who spread it to non-Jews, was among the most highly-educated Jewish scholars of the time. The Romans and Greeks were not, as far as I know, antisemitic any more than they were anti-anyotherbarbarians. OK, maybe they liked them a little less after Masada, but you kind of have to give them that one...

While I do understand that antisemitism is a later development that had a number of causes besides Christianity, I can't speak to that portion of your question with authority. Perhaps u/estherke will stop by?

Antisemitism has been around as long as Semitism, and stems from several sources. During the rise and rule of the Roman Empire, the Jews were the most devout and self-isolating religious group in the known world. All religions were accepted and integrated to the panthesitc Greco-Roman world, and even Judaism recieved a shrine/temple in Rome alongside the temples of every other god. But the Jews refused to incorporate any other beliefs into theirs, and adhered to their own rules, well, religiously. This is where the separation, mistrust, and persecution starts. Later on, after the rise and bloating of Christianity, they were persecuted by the Christians themselves. The Catholic church promoted poverty as a form of worship, and since merchants and trading were thus deemed sacrilegious, the Jews stepped in ( since they had no rules against this in their religion) and took over business and trade. This is where the generalization and steryotype of Jews being "penny pinchers" and wealthy business owners came from. There are many more reasons and accounts and periods of persecution and antisemitism, but a lot of it stems from their inherent self-isolation and religious devoutness. Antisemitism is just ignorance and scape goating throughout all of history.

Both comments match up with what I'm already aware of - that'll have to do. :) Thanks, guys!