Probably the military does not keep such stats, but is CO running higher among Christian and atheist troops; or higher among islamics?
..TM7
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You are correct, I can find no formal stats, but I can speak anecdotally. I have taken Muslims with me on both combat deployments, and spoke extensively with them prior to deployment during our workup combat training. I made it a point to address them individually understanding the unique strain their status would place both on them and their fellow Marines. To a man, all of them stood with their fellow Americans when it mattered, and I think that's the key. Let us not forget also, that there are literally thousands of Iraqi Muslims in uniform fighting alongside of us against other Iraqi and insurgent Muslims, and thousands of Afghani Muslims fighting alongside of us against other Afghani and Talibani Muslims, and thousands of Phillipine, Indonesian, Somali ... to be a Muslim does not mean you cannot take up arms against other Muslims, as long as the cause is just. They are free to exercise their own conscience in determining whether its just.
Of the COs I've screened, none of them had strong faith or religious tradition prior, just vague relativistic convictions with no underpinnings. None of them had converted to a recognizable philosophy or religion since joining. 3 of the 4 came from single family homes, raised by their Mom. All of them joined to prove to the world that they were a man, to serve their country and satisfy a patriotic urge. All of them had been in less than year, had not deployed before, and were vocal during the first couple months of unit training, which is brutal and often a time for hazing. They had all heard horror stories from our one pump chumps - LCpls with stories of shooting women in the face and burying the bodies in the Euphrates - none of which were true, and the tellers had in fact seldom left the wire. This is also the time when dozens will ideate about suicide, file for humanitarian or compassionate transfer or discharge, have emotional breakdowns (one ran out onto a live fire range), claim homosexuality (wise First Sergeants place a phone in front of them and tell them to call their Dad and come out of the closet - nobody made that call). In other words, the reality of what they signed up for has kicked in - it ain't Halo, there's no reset button. That blood you see where you stuck your buddy with an IV, yeah you're going to be seeing a lot of that, probably your own. Ooh Rah, get some.
Everyone is afraid from the salty Gunny with 7 combat tours down to the boot PFC, and the intensity of the training reveals how people deal with it - that's when the CO requests get filed. Its like clockwork.
A 5th one was a sociopath who conscientiously objected to the restraint we would place on him and not allow him to satisfy his homocidal urge. He admitted to me that all his life he wanted to kill someone, but knew he'd go to jail. So he joined the Marines to "get some." When we taught him the law of armed conflict, rules of engagement, and warrior ethics he became disillusioned and requested to see me. He thought it would be like the movies, indiscriminate killing of anyone and everyone, and he was disappointed. We booted him fast.