The Islamic Republic has been in power since the Carter years. This means anyone born after the late 1970s has spent their entire life under this regime. When the Shah fell, there were a significant number of people who thought they were protesting for a democracy.
If you think people form their view of the world starting in their teens ( or somewhat earlier for some), that would mean that everyone not born before 1970 came of age under the Islamic regime. It may be that some were very quietly influenced by their elders who knew a more secular time or by the prevalence of things like the internet.
Personally, I had an Iranian born office mate in the early 1980s who had been studying in the US when the Shah fell. By the time I knew her, she was a green card holder married to an American on the path to citizenship. She was brilliant, beautiful and an extremely nice person. She was one of many secular, extremely well educated modern people. I would imagine, that like her, there were many who are now part of a Persian (the word she chose to describe herself) diaspora. The question is how many remained.
Unlike many countries who have their roots as a country in lines drawn in colonial times, Iran has been a country going back many centuries. It has its own culture, with beautiful art and fantastic food. There is very great pride in their culture and people.