I speak as a former Marine, who is very proud of his service. The biggest thing the Marine Corps is reacting to is the fact that he is doing this in public.
One of the most important things you learn as a Marine is we are all a family, and you can do things around family members you cannot do in front of other people.
This incedent is basically the same as walking around the mall in your underwear. It is fine in your living room, but the mall is not the place to do this.
I find the lyrics behind Hadji girl to be slightly amusing, slightly annoying, while I have never seen the video, I can understand the sentiment behind the Marine Corps reaction to be nothing suprising.
A similar example is finding a Marine off base, outside of a combat zone, wearing camoflage utilities.
Look around Camp Pendeleton at lunch, off base you will not see one set of cammies outside a vehicle.
As to the reaction to CAIR, the Marine Corps has always had a great relationship to the press and are very pro-active in maintaning that reputation they have spent 230 years building. Reading the accounts of Belleau Wood, Iwo Jima, Khe Sahn, and even Fallujah the Marines have always held themselves to a higher standard, and God willing always will. This is even reflected in the press accounts, and historical accounts, (not bastions of pro military thinkers).
All of these incidents are examples of people going above and beyond, and the fact of the matter this young Corporal fell short, if he did it only in front of other Marines, it would be no big thing, but he did it publicly, so now he has to be punished publicly.
Now you are free to tell me to go pound sand, but I just wanted to state my two cents.