The hostility we currently associate with Iranian-Israeli relations didn't really come about until after the Gulf War in the early 1990's. Whilst the post-revolutionary government in Iran certainly amped up the anti-Israeli rhetoric, the strategic hostility wasn't evident during the 1980's and the Iran-Iraq War. That is to say, whilst they weren't friendly, there were enough pragmatic common interests not to preclude working with each other.

These 'common interests' basically equated to Saddam Hussain. For all Iran's revolutionary fervour and fiery pronouncements, Israel did not view Iran as a fundamental threat largely due to how far away it was, and the fact that it wasn't viewed as an 'Arab' state. At this point, Israeli foreign policy was concerned with neutering the Arab bloc, seeing it as the most fundamental threat on account of the proximity of Arab states to its borders. To Israel, the biggest threat of them all was Iraq under general madman Saddam, who on top of being a general dictator was also massively anti Israel and obviously anti-Semitic. Therefore Israel feared an Iraqi victory in the Iran Iraq War would empower Iraq to the extent to which it could pose a direct security threat to Israel. Ergo, it supported arming Iran. During the 1990's you see a 180 degree repositioning of Israeli foreign policy and a shift in focus to working with Arab states to neuter the 'Arab bloc' and the designation of Iran as the primary strategic threat.