I lived for decades in Detroit and the Detroit area, which features large communities of Lebanese Americans, many of whom are traditionally Christian. One thing I noted is that as a group, Lebanese immigrants of Christian heritage seem to oppose Israeli occupation of Palestine as fiercely as Muslim immigrants from that region oppose the occupation.
Sit down with a group of Lebanese Christians and Lebanese Muslims, and I don't think you'll find much divergance of opinion with respect to support for the rights of displaced and oppressed Palestinians.
You make a really important point!