I think I see what you're saying. It has always bothered me that Christians can so easily flip-flop between the Old and New Testaments. This seems to me to be an adulteration of both. Example: Psalm 139 ""Oh Lord, shouldn't I hate those who hate you? Shouldn't I despise those who resist you? Yes, I hate them with complete hatred, for your enemies are my enemies." I found this in a little booklet entitled, "The Book of Hope" distributed by a local Christian church.
As to this idea of "Christianity as a stand-alone new Jewish theology", this is a new thought for me and perhaps your right. Why else would the Old Testament play such an important role right down to the overwhelming support of Christians for the State of Israel and the Jewish right to land that was occupied by other folks? That's like the U.N. pronouncing that the State of Wisconsin no longer exist. It is now going to be governed by other folks and current residents have no say in the matter or the government. Or like the U.S. saying to the American Indians, "This land is now the State of Wisconsin and you're going to have to move."