I'm not making any moral equivalence, this is an academic equivalence. (Much like what my Pope recently did).
Both coerce people to worship God.
What makes the Blue Laws different they encourage people to go to church, whereas the Iranians force people to go and pray. And this is a big difference.
The second big difference is Blue laws can be justified without resorting to "God's Will."
I tend to agree with most of your assumptions. While they deny it, if you put a polygraph on the average religious activist and ask them:
Do you believe government officials should rule and make laws based on a religious law?
Should government officials pray that they are context?
Should religious law trump civil law?
Should our government leaders seek to be devinely guided?
All would answer yes to the questions. And all would be answering that they would want a theocracy because the above is the classic definition of a theocracy.