Iran is one country where we really need to make an exception between the Mullahs and the Republican Guard on one and the general population on the other.
The people are really a moderate, semi-Islamic lot who trace their civilization to pre-Islamic times which was when they saw their golden age. Shia’s are not Salafists. They generally tend to be a more modern bunch. As much as we hate the Hezbollah, if you ever went to Lebanon, you won’t see women forced to dress conservatively, nor a crazy lot wanting to apply Shariah on everyone like we saw in Egypt. Same for Syria - the Alawites are far more easy on day-to-day personal freedoms so long as the regime is not threatened. The Shiite countries also tend to be far more secular in how they treat non Muslim minorities.
I think that many in India see the situation in the way you set out, and indeed, see Iran as a great contrast to their unstable/threatening neighbour Pakistan.