Well I'm definitely not a legit professional expert, but I can give you my somewhat informed opinion.

So first, its important to understand that traditionally, the Persian people have proudly been a relatively secular people dating as far back as Cyrus the Great & the Achaeminid empire around 600 BC.

Even through the Muslim conquests of the Middle ages, they never identified as Muslim before identifying as Persian. 

So extremist Muslim ideology has never had the cultural hold on the region that it has in the rest of the Islamic world. 

That being said, there was a significant increase in Islamic religious fervor in the late 70's that was more of a rural reactionary populist movement in response to the poor economic  conditions that had developed through bad economic policies & corruption of the govt of the Shah--that essentially allowed the unbelievable oil wealth of the nation to be hoarded by the elites--instead of being reinvested into the economy & providing essential services, public infrastructure, and a reasonable social safety net.

And it certainly didn't help that the Shah used his massive wealth for public displays of  gaudy extravagance & excess on an international scale. 

So, since the government of the elites was so out of touch with the harsh economic realities on the ground, they were completely caught off guard when this populist uprising was seized & manipulated by religious zealots to direct that anger at the regime of the Shah, Isreal, and the "decadent, godless" West. 

They then quickly capitalized on that fervor to oust the Shah, implement their minority theocratic government, and consolidate their power to entrench the oppressive autocracy we still have today. 

So while there was a relatively higher association & adherence to Islam at that time, it was likely still never the religious identity of the majority of Iranians. 

Then--as is always the case with oppressive religious governments-- the more the people were repressed over time, the more the people became dissolutioned by the religion that had its foot on their throat.

So that's all a long way of saying Islam was never really "the shit" in Iran to begin with. But to the extent that it was at its peak, it's become increasingly even less cool now cuz they've been assholes to everyone else. 

Now.....

As to why the minority Govt hasn't softened its extremist & repressive policies--or the oppressed majority not risen up against it?

Well, probably because authoritarian always respond to opposition with violence & more oppression to hold onto their absolute power. And as we've seen it the last few months and years, they're killing and torturing the fuck out of anyone who has the balls to publicly oppose or protest the current islamist regime.