You are making the mistake in thinking that the only true Jews are those who reject Jesus as the Messiah. The Christians of Israel are not ethnically gentiles but rather the descendants of the first generation Jews, like Peter and Paul, who recognized Jesus as the promised Messiah of Judaism, i.e. they are ethnic Jews. If you are to maintain that the Holy Land is still promised only to ethnic Jews, then from a Christian prospective the Christians of Israel have as much claim to the land as their non-Christian cousins.
We also don't know how many Christians in Israel really support Israel. I know some "Palestinian" Christian groups who are jsut as anti-israel as the Muslims are.
This is largely a myth. There were many non-Jews in Israel during Second Temple times, including a very large Greek community, and huge Samaritan community.
Some Jews in ancient Judea certainly converted to Christianity. But the Jewish Church basically got annihilated during the revolts against Rome. Today's Israeli Arab Christian community largely descends from a combination of Greeks, Crusaders, Samaritans, and pious pilgrims throughout the centuries. Jews are likely a pretty small portion of the community's ancestry. If it makes you feel better, Samaritans are largely Israelite (though not Jewish). And those who weren't killed by the Byzantines largely converted to Christianity and, later on, Islam.