First let’s distinguish between Palestinian Christians and those who truly follow Yeshua as their L-rd and Savior. Many times you’ll hear the term “Christian” thrown around but in Israel and the surrounding countries, Christian simply means you were born into a Christian culture. It doesn’t mean that the person has a right relationship with Jesus or has accepted Him as their Messiah. So in the following I’ll speak of Christians who don’t know G-d in their hearts as “Cultural Palestinian Christians” and those who love Yeshua as “Palestinian Believers”
Prior to the establishment of the Jewish state of Israel, approximately 20% of Palestine's population was “Cultural Palestinian Christians”. This is reflected in the large number of Palestinian leaders that are “Cultural Palestinian Christians”. This includes Hannah Ashrawan, Edward Said and Arafat's wife. However, the Cultural Palestinian Christians were also often found in the more affluent segments of Palestinian society which generally fled the country in conjection with what they deceivingly call Al Naqba (Arabic disaster; the creation of Israel and the ensuing refugee crisis). Thus while Cultural Palestinian Christian voices are often heard from the Palestinian diaspora, the Cultural Palestinian Christians presence in Palestine is dwindling.
There are Cultural Palestinian Christians who subscribe to many different Christian sects, including, but not exclusive to: Roman Catholic, Greek Orthodox, Russian Orthodox, Egyptian Copts, Methodists, Lutheran, Anglican, etc. There are many groups, comprising a minority of the Palestinian population. These people are rarely heard from in most debates about Palestine or its future. Many terrorists are from Cultural Palestinian Christian factions such as The Popular Front for the Liberation of Palestine which was founded by George Habish who has since died. They advocated and still advocate the murder of innocent Israelis.
As for Palestinian Believers, they have a difficult time in Israel. They are a rare breed and have the hand of G-d upon them. I have many friends in the West Bank who love Yeshua (Jesus) with all their hearts. Needless to say they are pro-Israel. That means more then you might think. I lived in Beit Sahour for many years, it's one of the most dangerous places in the region. Beit Sahour (The Shepherds fields of the Brit Hadasha- New Testament) is in the West Bank located just below Bethlehem. I've watched as Palestinian mobs overran a nearby house and killed the family with large knives simply because they were thought of as collaborators with Israel. Many times these accused of collaboration are Christian Arabs. Moslems insight the crowds against them and falsely accuse them of collaboration all the while knowing they are innocent of the charge.
It's a difficult place for them, please keep them in your daily prayers.