From what I have seen, it depends on the day. Every time that I have flown in, they have looked through my passport (most likely for an Israeli stamp). I have heard of some people having issues, but I am fairly sure that there is not an official policy that you cannot get in if you have an Israeli stamp in your visa.
For anyone that wants to go to Israel but still wants to be able to travel to the Middle East, there is a nice little trick. If you staple a blank piece of paper into your passport, they will stamp that when you fly into Israel. After you leave, just rip it out. I have not personally tried it, but I know several people who have.
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