Basically to claim that the new religion Christianity was valid it needed to:
1) base itself off an older religion. At the time of the start of Christanity, age of a theology was that gave it validity. So claiming it's based in Judaism gave Christianity a fighting chance to get accepted.
2) However it's a different religion, with a lot of opposite believes to Judaism. So it was claimed to be replacing Judaism as a better, newer version. All this was while being quite different. Also it was much better to project all the upset with the Roman persecution onto the much less powerful Jewish group than saying straight out loud that the Romans were harming Christians. (So that's why in the Christian Bible Jesus is claimed to be killed by Jews, when it's not logistically possible based on historic information in the bible, and is very possible to be a Roman trial and killing.)
3) So Christianity in it's implementation (not in it's core theology but in how it was implemented) developed an elaborate and complex way of describing itself as "replacement" for and "better than" Judaism. With that came intense put downs of Judaism and Jews. The funny thing was that as Christiaity took over Europe and so many other groups' theology diappeared, Judaism was kept alive but crippled as part of this theme. Hard to prove you are better than, and replacing something, if the something (judaism) disappears. Meanwhile you have to revile it and keep it down. (A great chance for power hungry people to take advantage of this misuse of Christianity and abuse it for their own purposes and abuse Jews.)
4) With that comes the projection onto the Judaism and the Jewish population of every morally evil trait a society can think of and doesn't want to find amoungst itself. So instead Jews because "evil" "money grubbing" "out to control the world" "hateful of Christ" and every other negative thing you can think of. That's part of why antisemitism can be so hard to describe. It morphs and adjusts to every new setting, and has such elaborate and non-descript hate concepts in it. (Compared to calling blacks "childlike" or "oversexed" and any other ridiculous but straightforward character trait intended to keep them enslaved emotionally.)
5) In the late middle ages, as religion was challenged by scientific reasoning, hate of Jews shifted from a reviled group to the more scientific claim of genetic / inherited inferiority. Before then, you could leave the "evil" by converting out of Judaism. With that shift opened the door for the Nazi-style decision that all Jews must be wiped out. It's also when the hate of Jews changed from anti-Jewish to anti-semitism. The term was invented by a hater of Jews to make it sound more scientific and genetic based. (Since Hebrew is a semitic language.)
Other people gave accurate answers. I hope this adds to them.
Sources.... I explain a little in the comments. To continue:
This site used to have a wonderful set of pages explaining a lot. It's from the National Catholic Holocaust Education Center. http://www.setonhill.edu/ncche/resources Those pages were taken down. Now revisiting the site today, I've never seen the current first article. It's a teaching guide that goes into a lot of detail. Here's one blurb from it:
"In its quest
to establish itself as the superior bearer of
God’s Covenant, the early church interpreted
the Christian Scriptures with three decidedly
anti-Jewish themes. The church fathers claimed
that according to scripture:
the divine election of the Jews as the chosen
people of God had passed to the Christians,
2. that God had rejected the Jewish people, and
3. that the Jews were directly responsible for
the death of Jesus (the charge of “deicide”)"
For my fifth item about the shift from religion to science, one of the many sources was the book "The Popes Against the Jews." It's written by a well respected historian who was let into the Vatican vaults to research for it. It only covered a limited sliver of concepts, but makes convincing arguments using original documents.
On the NT's descriptions not fitting properly into Jews having done it -- there are a number of sources as well. It was a big study & insight that shifted the Jewish-Christian relationship in the 50's, 60's... part of what fed into Vatican II. The Jewish Sanhedrin met and had rules that make the likelihood of it happening as described, as likely as the US Supreme Court deciding a landmark death penalty case in one of the judge's backyards on a Sunday after a BBQ with plenty of alcohol. The rules are in the Talmud & well-known in Jewish study. The application to the NT & working with Christians was very new.
On antisemitism being about projecting on morality, it's something I heard recently, but it gives a summary to it that fits completely. http://www.tabletmag.com/jewish-news-and-politics/183033/israel-insider-guide?fb_comment_id=fbc_710619675659231_711027128951819_711027128951819#fecd11f44fbbe
To see the list of accusations at Jews, a good source is the Nazi favorite forgery book "The Elders of Zion," still motivates antisemitism today. I haven't read through, just skimmed. It's gross and irrational. A few sites with decent descriptions -- well, I'm not allowed to post more than 2 links, so I'll post these in the comments below.