I'm glad others have responded to you with some evidence, I have seen some of it before but am going mostly on stories from Iranian family members who have been arrested and harassed and subject to physical violence for not covering their hair properly.

Yes, it is much, much worse than in places like the US, it is carried out by state agencies like the morality police and by pseudo-state entities like the "Basij". As others pointed out, when you.move outside the cities things often get less 'civilised'

I understand that people don't want to fall into the trap of prejudice, but things are materially worse in places like Iran, and drawing parallels with how women are treated in the west is not helpful. We have problems, we don't have the morality police or relgious militias, at least here in the UK