"And what you mentioned is called Conflict between Traditions and Modernity which exists in the Iranian society."
Call it anything you want. Ask any Muslim which is more important, Islam or democracy. All will say Islam. Any who choose democracy are not true Muslims.
Well you are saying "Ask Any Muslim"... It is right but
most Iranians I know, do not consider themselves as Muslims
You might be interested in talking to some of them.
Iranians want to be called Persians or Iranians and they try to keep away from their Islamic identity!