The thing that confuses me is the idea that one God is Jewish and the other is Christian. The way I was raised is that it is the same God in both the Old and New Testaments, and at some point, for some reason, God changed how God dealt with the Jewish people, moving from a law-based relationship to a redemptive one.

The first Christians, after all, were Jews (and devout Jews, at that), and they had no interest in sharing their belief in Jesus Christ as Messiah with non-Jews. As the account goes, it took a divine revelation from God to the Apostle Peter for Peter to preach the gospel to a household of Gentiles who were interested in learning more. Before that, Christianity was a purely Jewish thing. Christians who use Christianity to justify their anti-Semetic prejudices totally miss that aspect of their religion's foundation.