But the ultimate winners among the Christian factions were the ones who followed Paul in renouncing the covenant of circumcision and declaring that the Jewish god had changed [his] mind and didn't want to be just a tribal God any more.
Such a God is in this context a Christian invention. The Jewish God is still there, still God of the Jews.
Jesus was Jewish, and believed in the Jewish God. The Christian religion spun off of the Jewish religion, and shares the same God. Jesus brought a new message from God to new people. The old message to Jews was "eye for an eye" (though "thou shalt not kill" was part of the 10 commandments and were brought down from the mountain by Moses as rules for Jews) and the new message to Christians is "turn the other cheek." This is because Christians, in modern times, have nuclear bombs, so if they are hot headed idiots and make wars against the wrong people (such as the war in Iraq), they could do serious damage. God sees the future and knows what mistakes humans can make.
In addition to restraining the violence of Christians, God released them from the requirement of a bris and dietary restrictions. Though the bris is a good idea, even in modern times, because it is more sanitary. In modern times, with refrigeration, and better medicines, pork restrictions are not as necessary.
So,
religiously, Christians are Jews, but without the restrictions, and the Christian God is the Jewish God. Ethnically, of course, Christians are not Jews (but Arabs are Semitic, just as Jews are).