The first Christians were Jews. They would have, very much, believed themselves to be Jewish (religiously as well as genetically). The followers of Jesus Christ were a sect (denomination) within Judaism. However, there came a point when the Christian understanding of God and God's relationship with humankind was so radically different to that of mainline Judaism that it was as if Christians worshipped a different God to the God of the Temple and synagogue. Christianity became a new and separate religion.
I believe this tipping point has now been reached by American, fundamentalist Evangelicalism.
To put it simply, they no longer worship the same God that the rest of us (Catholic, Protestant, Orthodox, whatever) worship and, to be fair to them, they do not believe that Christians who are not part of their sect worship the God that they do.
We are agreed then. Let us go our separate ways so that the people of the world are no longer daily confused as to why a loving God can be so goddamn hateful.