I think an honest assessment of the history reveals that the Islamic Republic has been far more hostile to Israel and far stabler than the Shah, who oversaw a deeply unpopular monarchy and was deposed by his own people
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.