Judaism
Christianity was originally a sect of Second Temple Judaism, but the two religions diverged in the first century. The differences between Christianity and Judaism originally centered on whether Jesus was the Jewish Messiah but eventually became irreconcilable. Major differences between the two faiths include the nature of the Messiah, of atonement and sin, the status of God's commandments to Israel, and perhaps most significantly of the nature of God himself. Due to these differences, Judaism traditionally regards Christianity as Shituf or worship of the God of Israel which is not monotheistic. Christianity has traditionally regarded Judaism as obsolete with the invention of Christianity and Jews as a people replaced by the Church, though a Christian belief in dual-covenant theology emerged as a phenomenon following Christian reflection on how their theology influenced the Nazi Holocaust.
Antisemitism in Christianity
Mainstream Talmudic Rabbinical Judaism today directly descends from the Pharisees whom Jesus often criticized. During Jesus' life and at the time of his execution, the Pharisees were only one of several Jewish groups such as the Sadducees, Zealots, and Essenes who mostly died out not long after the period; indeed, Jewish scholars such as Harvey Falk and Hyam Maccoby have suggested that Jesus was himself a Pharisee. Arguments by Jesus and his disciples against the Pharisees and what he saw as their hypocrisy were most likely examples of disputes among Jews and internal to Judaism that were common at the time, see for example Hillel and Shammai.