See the recent 60 Minutes episode on Palestinian Christians in Israel. Bethlehem is now down to 18% Christians (it used to be nearly 100%). The Old City of Jerusalem had 30,000 Christians thirty years ago but is now down to just a handful.
The problem is not Israeli policies that specifically discriminate against Christians. However, the miserable conditions of living in the Occupied Territories make life undesirable for all of its residents. And those who can get out, do.