If we put the "religious right" in charge of drafting a new constitution for the United States, do you think that maybe they'd want one a bit more overtly religious than the one we have now? Maybe one that specifically said abortion was illegal, prayer was okay in schools & other public places, same sex marriage and sexual immorality were illegal, etc.?
I'm not saying that having Islamic law enshrined in the Iraqi constitution is a good thing; from what I've seen it's not that compatible with human rights. HOWEVER, if you have at least a third of the drafters who are very religious, and that is their religion, I don't know how you would expect anything else -- unless maybe we just spelled it all out for them and made them take what we wanted them to have.