As far as the Christians are concerned, I think it started somehow like this:
1.) First there was no church and no theology, but only small groups of likeminded people.
Some of them came from the Jewish tradition, some from the Roman tradition.
2.) Then some people started to construct some theological framework and the questions arose if or not & how far the Jewish traditions (circumscision, rules reagrding food, Sabbat,...) should be followed, since Jesus had been a Jew.
Those who had no Jewish background of course did not care much about Jewish traditions, and I think it was Paul who insisted that those did not have to adopt them.
3.) In the first centuries Christians were a minority having to get along with the Roman authorities.
Therefore perhaps there is a tendency to play down the role of the Romans (Pontius Pilate) in the trial & conviction of Jesus and to give grather attention to the Jews (Caiaphas).
4.) In the Middle Ages Christianity was the dominant religion.
Work life was organized in form of guilds, everyone who wanted to work - for example - as a joiner had to be member of the joiners-guild.
Guilds did not accept non-Christians as members, so Jews could not get jobs - the only profession open to Jews was moneylender.
As moneylenders they drew hate from those who already had difficulties to survive at all, most people were very poor.
Those who had more than enough were clever enough to use the prejudice of the poor mass and directed their hate towards the Jews, away from themselfes.
Once a group is segregated from society-mainstream it is only to easy to make those people responsible for everything that's going wrong.
And prejustice is easy to propagate but hard to get rid of.
