I have a Muslim friend who joined AAA about 10 years ago and has been sober ever since. He has no problem with the Christian message which he does not buy into except to the extent that like in Islam it provides a spiritual dimension to their struggle. And, has he points out, it's not the religious message that is most important in saving you from your addiction, its  the people you share your affliction with.
http://boreal.ca/Iran/SohrabBar.htm