At the risk of getting flamed, I'm going to go out on a limb here; respectfully.
I was in Iraq as a soldier on OIF2 and the Kurds I worked with were also Muslims and they risked their lives on my behalf many times. The fact that I was a professing Christian did not deter them nor did they treat me as anything less than a friend. They showed gratitude at every opportunity for setting them free from Saddam.
The Kurdish children would bring me flowers and say "I love you Amriki". Kurdish men would risk their lives to help us, their Peshmerga were very brave fighters who had opposed Saddam at the peril of their own lives. I can't go into a lot of detail lest I possibly violate OPSEC, but please understand what I'm saying.
It is wrong to paint all of Islam and all Muslims as terrorist sympathizers. Some of these Muslims are in fact our allies right now and although I don't agree with their religion, I learned to differentiate and sincerely hope that you will also.
Welcome to FR and thanks for your service. Not having been in Iraq I'll defer to your experience. I think you'll find concurrence here with your view of the Kurds.
I hope that Muslims work this out amongst themselves. I am not seeing this happening though. Lock and load, IMHO.