Christianity announces a new covenant to replace the old, the baptism replaces the circumcision. Only through baptism can Jews continue to be the people of God, according to Christianity. A Jew who continues the vacant covenant by circumcision is no longer manifesting a connection to God, but rather disunity - in the eyes of Christians.

As for Christ being Jewish, yes, it makes sense for most people to say that. But for Christians nothing could be further from the truth, if you mean to imply that Jews (the circumcised) are just the same thing (God’s chosen people) before and after Christ. Some therefore would like to talk about Israelites (members of the 12 tribes of Israel at Jesus’ time and before) to separate them from the Jews, ie those who rejected the Christ.

Besides following a vacant covenant, there is added distance between the Israelites at Jesus’ time and later Jews, as those who remained Jews after Christ made the Talmud about 400 later, a compilation of exegeses that explicitly targets Jesus, saying for example that Jesus is in hell.

When it comes to the criticism of the Jewish religion itself it is Talmudic Judaism Christians criticize, something that did not exist at Jesus’ time.

I’m just outlining where the distance and difference lie. The precise and direct reasons for resentment of the Jews varied of course a lot over time.