In Theory, Would a Peaceful Islamic Caliphate Have Merit?

[I spent the winter writing songs about getting better]

However, I don't think there is what we tend to call "moderate Islam" either.  There are people who take religion less seriously and their rationality and humanity guides them to keep religion from clouding their judgment.  There is no moderate, progressive version of Islam, there's no reform Judaism or Episcopalian equivalent in Islam.

The Bektashi might qualify.

And to the OP: No.

[I spent the winter writing songs about getting better]

I should also point out that unless it includes Spain (and Israel) it's not a Caliphate.