For one thing, a person's political beliefs often have nothing to do with their government's position. Has it never occurred to you that a Muslim is leaving his country to go to Kashmir because they've a;ways preferred Democracy and know they can't get it at home?
You're operating under the premise that all Muslims are evil, terrorist, America/Democracy haters who only do anything if it will undermine the stability of whatever region of the world they're in. Most Muslims are pretty much the same as most Christians, Jews or anyone else. They want a good home, a chance to be prosperous and take care of their family, and not to be hassled by idiotic people with myopic views of the world.