Pretty unlikely for Iran and Israel to fall out. The Shi'ites just aren't as opposed to an Israeli state as the Sunnis are (especially Wahhabiist Saudis), and - as has been mentioned - it makes a lot of geopolitical sense for Iran to ally with Israel against their common enemies in Iraq and Saudi Arabia. Both have a vested interest in destabilising Syria, too - Israel want a weak state on their borders, whilst Iran want to be able to keep their links through to Lebanon and ultimately the West open (and forcing Iraq to look both ways doesn't hurt, either).
That said, if you really want to get this guy in charge (Khamenei? Khomenei? Something with a kh- at the start, anyway...), then perhaps a way to go about it would be to have the Soviet Union collapse in the 1950s or 1960s, or at least go into a major decline. OTL, the end of the Cold War opened up the Pandora's box of fundamentalism in Central Asia, and whilst there probably wouldn't be anything as serious as the Tashkent Incident in this case, it would certainly mean that America isn't the only defence against the godless communists...