The only problem anybody has had that I know about is that soem Israelis have had more than normal security examinations. I know three Israelis who have flown EK transiting Dubai without incident. It is obviously easier and less of a hassle to use a non-Israeli passport that has no Israeli stamp, just because there are no questions that way. There are Jewish residents of every country in the region, though the ones I know are not observant and do not actively promote their ethnicity. Nearly all Arab countries ask for religion on visa applications and entry documents. I always put "none" and have never been questioned; that is in more than 30 years of Middle East travel and nearly a decade of residence in the UAE, Bahrain, Yemen and Iran.