I believe you're talking about the CIA backed coup in 1953.

This picture would have been taken during the period where Iran was ruled by the Western puppet Shah.

But the point still stands, tough to imagine the Iranian Revolution of 1979 if there had never been a Western coup and over 25 years of effectively Western rule.

Western policy certainly paved the way for the Islamic revolution, but encroaching Western decadence is not the reason why they're censoring women's legs at the moment.

Persia has historically always been a leader in academics, cultural exchange, arts, literature, engagement, civil rights, and philosophy, dating back to at least Zoroaster. It is only in recent decades that the regime has instead favored ignorance and isolation. The present state of Iran is the historical outlier, not vice-versa.

I think you're confusing a few things.

Was it the west that instigated a change, because they were greed for oil and didn't give a fuck?

Yes.

But who actually took power? Conservative Muslims.

Fuck all monotheism.

The intolerance of narrow monotheism is written in letters of blood across the history of man from the time when first the tribes of Israel burst into the land of Canaan. The worshippers of the one jealous God are egged on to aggressive wars against people of alien [beliefs and cultures]. They invoke divine sanction for the cruelties inflicted on the conquered. The spirit of old Israel is inherited by Christianity and Islam, and it might not be unreasonable to suggest that it would have been better for Western civilization if Greece had moulded it on this question rather than Palestine

https://en.m.wikipedia.org/wiki/Criticism_of_monotheism