I looked at the CIA Factbook but wondered if I could really trust it. Saw the other link I posted and wondered how there can be such a huge disparity?
My link says 20-30%. Wiki / CIA say 90% ish. A GAMAAN survey says around 50%. With an oppressive regime you can easily envision a mindset where you may openly claim to be Shia, but perhaps hold a different view due to fear.
Reality is we do not know, but there is a clear incentive and motivation for Iranian leaders, or opponents, to lie.
https://en.m.wikipedia.org/wiki/Religion_in_Iran