Take voting rights. Switzerland was last of all the "civilized" democracies to establish full voting rights for women. Why? Well, the current voters had to vote for that constitutional amendment, and them being all male they had no big problem with denying women a vote. In the US plenty of states suffer from a similar dynamic where politicians actually keep a majority beyond what the population actually wants by making it harder for minorities to vote. All those things are not democratic despite getting voted on in supposedly democratic systems.
Tell that (for example) to Iranian- or Afghan- or Saudi women who must cover themselves in public, can't drive, and possibly can't leave the house without a male relative.
Or tell it to women in Texas, Idaho, etc., who are compelled to carry unwanted pregnancies to term — and then are largely left to fend for themselves after their forced births — because power-seeking radicals have democratically imposed "Christian" values about when an abortion is supposedly "murder."
To be sure, living in a society involves duties, not just rights. But some purported "duties" go too far.
And as to Idaho and Texas—who decides where “murder” begins? Me? You? Someone has to, right? What is the rule of decision? Why should post-Christian secular humanism provide the rule of decision instead of regular Christianity, or Islam?
The "elites" in Iran are the Shi'a hierarchy. The "elites" in the US are, in your formulation, people who went to college and who live in major US metros. These are not comparable sets. Elite control over US policy is implicit (one might even say supposed); elite control over Iranian policy is explicit and rigidly formalized. These are not comparable notions of "turned over to".
Imposing Islamic values upon themselves is not the issue — or the problem.