If a religion is pervasive enough to tell you which hand to use to wipe your butt, the chances are that things won’t improve when you throw out that dictator, such as Mubarak, Assad, or Gaddafi. Instead of a thousand flowers blooming, what you are likely to get in his place is a bunch of ragged bearded men brandishing AK-47s and insisting on more radical forms of religious fundamentalism. Since politics and then whole subject of governance is dictated by the Quran, there is no such thing as democracy or a constitution that does not comply with Sharia law. There is only religious fundamentalism or dictatorship: the dial does not go in any other direction.
My comments here are primarily restricted to the Arab countries and a few North African countries. For over half a century, Turkey has been a largely secular democracy (though with some Islamist leanings). The Muslims of Southeast Asia run the gamut from Pakistan as the most fundamentalist to Malaysia and Indonesia as more permissive.
With most flavors of Islam, there is no hierarchy: There are just a lot of imams contradicting one another. (The only exception is Iran, where there is a hierarchy of Ayatollahs with Khamenei in charge.)
When many of the Arab (and some North African) countries erupted two years ago, most Americans (myself included) had some foolish notion that the result would be an ultimate victory for liberal democracy. As it turned out, it was anything but!