My short answer is that the Persians and the Arabs would continue their centuries-old religious dispute over who is the proper successor to their Prophet.   That Israel is just a side show to that theocratic war.  

Or at least which theocracy should be Caliph.  "A caliphate (Arabic: خِلافة‎‎ khilāfa) is an area containing an Islamic steward known as a caliph (Arabic: خَليفة‎‎ a person considered a religious successor to the Islamic prophet, Muhammad (Muhammad ibn ʿAbdullāh), and a leader of the entire Muslim community."

"The Sunni branch of Islam stipulates that, as a head of state, a caliph should be elected by Muslims or their representatives.  Followers of Shia Islam, however, believe a caliph should be an Imam chosen by God from the Ahl al-Bayt (the "Family of the House", Muhammad's direct descendants)."