you are part right-- some of the buildings in Jerusalem and Bethlehem are run by the Arab Christians.. who by the way do not, I repeat DO NOT call themselves Palestinians.. they call themselves Arab Christians who are Israeli Citizens.. I know because I have met most of them.. and they live usually in the Jewish sector.. I have spent a considerable amount of time in Israel from 1995 through 1999 and had the pleasure of meeting some of the directors of the Holy Sites.. they are well liked by the Jewish populace and are repected for their kinship... Most of them originally came from Morracco and parts of Saudi..
Then, there are the Syrian Orthodox who are permanent residents of Bethlehem. Frankly, I can't imagine how they would even qualify for Israeli citizenship. First of all they don't live there. Second of all they are Arabs.
Be that as it may, there are elements in Israel who have the ambition of deligitimizing the presence of both Moslems and Christians in Israel, the West Bank, or any of the various other places that were part of Israel or under its control in recent times or in ancient times.
Folks in Lebanon, parts of Syria, a fair chunk of Egypt, Somalia, Yemen, Saudi and Cyprus better watch out, because over the ages Israel, or Judea, or Jewish tribes have controlled and ruled a substantial part of the Middle East.
I do believe, though, that the fellows with their eyes on Saudi are keeping their mouths shut at the moment! (ROTFLMAO). And these folks with these claims do exist. I have talked to some of them. They are quite serious.
And then there's the crew looking for the pure red calf!