This could become a very interesting and fruitful discussion thread if respondents can think outside the box as it were. I would like to modify what goesh said by saying that we do not come from a society that separates religion and state so much as church and state. It is the mistake of many to see the church or mosque (and what is done in worship) as one and the same with "religion." It is not, and never has been. It is merely a very small part.

Religion is what is believed and practiced during the week away from worship, and it affects everything from how we vote to how we raise our children to what we value. It affects people in Iraq just like it affects Americans (perhaps Australia is secular enough that the affect is minimal, although one might call this secularism, just another religion). But the point is that we can and should engage the "Mosque" without ever entering the Mosque. There isn't any reason we cannot appeal to aspects of their world view in our counterinsurgency, have our Chaplains meet with their Imams (it has happened before), and in general understand these aspects of the population.

There is also a darker side. In my disputes with Kilcullen over religion and insurgency, I have always tried to appeal to moderation: "some" people fight with religious motivation, and "some" people probably oppose those fighters with force also because of religious motivation. Religion plays as much a part of forming their world view in Iraq as anywhere else in the world. It pays for us to understand the religion and culture enough to be able to identify players early on and align ourselves with those who would build the state and carefully watch those who would not. This approach might have saved us from letting the horrible Moqtada al Sadr go in 2004. Sadr might be the downfall of the COIN campaign in Iraq. Chalk that one up to Paul Bremer, who clearly didn't understand the culture.

This isn't holy war. This is just plain ole' common sense -- that frankly, isn't so common sometimes. Any country boy out hunting knows that you must know your terrain, and in counterinsurgency sometimes that terrain is made up of people.