I think a less drastic POD could do the job, maybe like pushing some sort of diplomatic solution more, or another nation offering a haven for the Jewish people(Vietnam? Australia?). But I agree that the Shia-Sunni split may lead to trouble in Iraq.
Well, no Holocaust certainly would do it, or you might possibly have something like the Uganda or Madagascar plans being implemented (though I would say the plausability of that it is rather low, if not ASB). As to not having a Holocaust, just replace Hitler with some other right-winger who is slightly less anti-Semetic, and thinks the Nuremberg Racial Laws (which will go away after *Nazi Germany looses the war) are enough.
-Would the West support Lebanon against Syria? For how long?
Lebanese internal politics will be very different ITTL. The presence of Palestinian refugees and the PLO inside Lebanon, and Israel on its southern border (both of which amplified Lebanon's sectarian problems in OTL) will be removed, so the Lebanese Civil War might not even happen, and if it does it will be quite different from OTL. But as to the original question, I would say most likely yes. In the event of a civil war, the
National Pact (which was set up before the POD) will almost certainly produce a pro-western government opposed by Arab Nationalist (and to American minds pro-Soviet) rebels, so Cold War politics will dictate an intervention of some sort.
-The Turkish have had disputes with Syria over the Hatay Province and water disputes. Without Israel, could this lead to war?
Possible, but not all that likely. Syria is much less powerful than Turkey, and if they tried to invade Turkey to gain Hatay, they'd almost certainly loose.
-Why would more Iran-Iraq wars break out? I always thought that the war was more of a power grab by Saddam Hussein than anything else.
Well, I would say an anti-Shah revolution in Iran is still quite likely (his unpopularity had much more to do with his domestic policies than his support for Israel), so yes, its quite possible. In fact, I think the history between Iran and Iraq would likely mirror OTL to a large degree.
-Wouldn't no Israel butterfly Black September?
As their will be no PLO, yes.
To make a few more comments-Arab Nationlism was an essentially anti-colonialist ideal-Arab Nationalists resented Europeans for (in their view) promising independence to the Arabs in WWI and then carving their territory up and either directly colonizing it or establishing puppet monarchies. Thus, it will be a factor in Arab politics, Israel or no. Gamel Abdul Nasser will still rise, still nationalize the Suez Canal and be invaded by Britain and France, and probably be remembered in the Arab world as a very successful and positive figure without the disaster in 1967 to tarnish his record. In the Arab world, Israel is generally percieved as a European settler colony established by taking land from Arabs and giving it to Europeans (this perception-not blanket anti-Semetism-is behind much of the Arab resentment towards it). Its non-existence will likely take some of the edge off of Arab anti-Westernism, and will make the rise of Islamism much less likely (the Arab defeats against Israel largely discredited Arab nationalism, allowing Islamism to step into the vacuum). The Middle East will quite likely be much more peaceful place than OTL.