But is it Islam or theocratists interpreting Islam wrong?
Who cares? Makes no difference in practise. Again and again Islam produces problems, while it solves no real problems of the modern world. That's the result of millions of people trying to live their lives like it is 1000 years ago, or following a silly book written ages ago.
Same for dogmatic Christians, of course. At least many Christians have accepted that their faith is a personal matter, they can believe whatever but they should not tell others how to live their lives. When Christians insist on telling others how to live their lives they only produce new problems, like the abortion issue in the USA. Unfortunately, Islam today is too far from accepting that faith is a personal matter.
Best of luck to the women of Iran. It is such a pity that the country of Iran is under an autocratic, theocratic government for 40+ years now. They have only caused misery around the world supporting all the wrong people everywhere.