Who do you think the previous regime was? The Shah was installed by the US and was friendly to Israel. Under the Islamic Republic, Iran has been hostile to Israel and funded proxy organizations that have been in conflict with it.
Well also, about Pahlavi being deposed by his own people, who really knows.
They also need to maintain Western support. That's billions in both military aid and payoffs to neutral countries like Egypt and Saudi Arabia, plus diplomatic ties. Netanyahu's administration wants to maintain support from its own people too. Having enemies isn't a completely bad thing for those reasons.