Muslim Arabs can be singled out as invaders - and they were - but the Christian Arabs of Palestine/Israel have always lived there and predate the Muslim invasion. They are probably the native Jews who converted to Christ and survived the Roman war. The Arab Christians of Bethlehem are probably the decedents of the same Jewish families who lived there in the time of Jesus.
Every year my parish church gets a visit from the Christians from the Holy Land selling hand made products that come from the wood from the olive trees.