I would say that the answer is complex and varied. CBS  did an article on Christians in Palestine a while back. Some leave because of economic reasons – no opportunities  and too much difficulty crossing check points into Israel.   Some say because of the lack of security. Others say they feel like they are our collateral damage and are being forced to take sides .
In one article less than 3% said they left because of religious extremism. Why anyone would want to move to Israel is beyond me . If I were a Christian I don't think I'd move to Israel. I don't think Jesus really like going there either (Judea), in fact he referred to it as his his place to go and die. I think he preferred the Gallillee.