Most Muslims don't even know what their religion preaches and are just trying to live their lives regardless of who governs them or who preaches to them on their holy day. These are the innocents. They are basically children of their culture and know no other way.
I understand where you're coming from here. It's the ideology we're fighting, not the people. We've cured some rotten ideologies in the past. The point is, they're going to have to abandon their culture. It preaches death.
Our other past successful wars have followed a general pattern:
1) Identify the enemy
2) Attack all infrastructure, supply-lines, and outside sources of support
3) Engage the enemy military
4) Demoralize non-combatants
5) Isolate the command structure
6) Obtain unconditional surrender
7) Help with the rebuilding process
There are some very real psychological reasons that these steps need to be executed in order. By engaging in the 'hearts-and-minds' campaign before the enemy is defeated, we're setting ourselves up for failure.
The tragic part of this is that the ideology that needs to be destroyed is wrapped-up in their faith. For a full surrender to be made, all of their Mullahs will have to denounce Mohammed's rants about killing infidels. Those verses will need to be stricken from the Quran, IMO. The actual shooting may temporarily subside, but until that's done, Islamists will carry on to the eventual aim that we're all either converts, slaves, or dead.