The problem is what you do with the first passport when you travel. If you are searched in the arab countries or Israel they will find your original passport. To those who say no problem get a 2nd passport please think it through, you will either need to carry the original with you (to get back into Israel), or get the 2nd stamped outside anyway. Syria especially is very good at investigating stamps I know. If you lose your original or it gets stamped by Israel somehow and try and get a replacement that replacement passport won't be recognized by many arab countries to gain entry.

Thus this is a problem for all that do it. I have been to Israel and they are very careful to stamp the sheet of paper outside your passport (as is Jordan).