When I left TLV, the security people took one look at my UAE and Jordan stamps and started asking all sorts of questions about why I had been to those countries (visiting friends and sightseeing). I know both those countries set them off, because in talking to each other the one guy said to the other "blah blah blah UAE, blah blah blah Jordan".

And JOrdan is nominally a friendly country to Israel these days.

In the end, just go. The Israelis are remarkably cool with these things - just expect some questioning if it comes up. In the end, they just want to make sure you have no bombs or friends with bombs. Muslim countries, on the other hand, will be irritated if you show up with Israeli stamps in your passport. Best to get a new passport or use a second one for Israeli travel.

AFAIK, the only Muslim countries that don't care if you have Israeli stamps in your passport are Jordan, Turkey, Egypt, Tunisia, and Morocco. I'm sure someone will correct me if I'm wrong.