the Iran-Iraq war goes side ways, the USSR backs Iraq and the US is uneasy about it but can't politically help Iran, turns to Israel, Iran needs help badly its sending waves of boys age 15-17 with nothing but the Koran against Iraqi gunners hopping to clog them with bodies so the US uses Israel as an Arms middle man, Iran makes Arabs and Sunnis as their buggy men rather than Israel and the Jews, Israel became the friend against the Arab devils, see Israeli Air Force do supportive bombings for Iran.
Some of this actually did happen in OTL, problem is it couldn't have manifested in greater Israel-Iran relations, Khomeini was plenty happy with the "puppet of Satan" line for Iraq and applied it just as readily to Israel, Israel largely involved itself to keep the war going and either side from really winning over the other, or even worse gaining an advantage that would threaten Israel down the line.
For example, the Soviets did indeed back Iraq in the Iran-Iraq War, remember that Iranian revolutionary Islamic ideology was just as hostile to godless communism as it was to pro-American ideologies. The US didn't peddle nothin' to Iran and it wasn't liable to do so through a middleman, that idea operates off the perception that the US wants to back a side but cannot for various reasons be seen backing it. Like how it funneled goods through the Pakistanis for use against the Soviet Union. The US hates Iran's guts now, it has everything to gain from the Iranians LOSING the Iran-Iraq War, not winning or even maintaining status quo as per OTL, plus the Soviet Union's under Gorby and the Cold War is slowly dialing down in general, this is a conflict where the Soviets and the Americans do actually stand to benefit from backing the same side, it isn't just some Cold War bush war where sides can be easily picked, it's an issue that one side hates both countries and the other can be cultivated AGAINST that other country, that was what was going to happen.
Also the Israelis did indeed bomb Iraqi facilities during the war, though these were largely operations designed hugely with Israeli self-interest in mind that the war facilitated, it was not because of any solidarity with Iran. Iraq developing a successful Project Babylon or worse a nuclear weapons program that turns Tehran into a smoldering crater or worse given the probability of Saddam happily tossing out nukes in the Middle East once he has them is simply not in the cards for Israeli policy, because surely the defeat of one great rival of Iraq would surely mean that Israel's head would be up next for the chopping block, at the very least the Iraqis could (if they were smart enough to avoid picking a nuclear fight with Israel) exert some pressure on Israel to get out of the Occupied Territories or recognize the Palestinians as a state. Of course this would largely be political opportunism to weaken Israel's position and hopefully give them in Palestine a friendly state indebted to the Arab states that makes a perfect springboard for invading Israel.
Also the term you are looking for is *boogey men*, problem with the Mideast is there's a lot of conflicts many of which are so entrenched as to be almost incapable of superseding the others. An post-revolutionary Iran allying with Israel is implausible given the circumstances, also remember that Israel is a US ally and that Iran had great relations with Israel under the Shah, both of which will be seen as something tainted by the Americans by violent reactionaries like Khomeini.