Isn't Iran as Islamic as you can get without going into Taliban territory?
The government is theocratic and strict, but the average Iranian civilian is actually pretty liberal and modern. It is apparently quite easy to avoid the wrath of the government, so if you don't do something suicidal
like being openly gay, you can go and live your life in peace.
Source: I have an Iranian friend and also a coworker, they are about as western as you can expect. One is even an atheist. Nice people, but they have huge blind spots to the bad stuff in their country though...