Islam is not a legitimate "denomination."
It is a false religion - one which enslaves millions.
And, has lead to the murder of thousands of innocent Americans.
The criteria that the government uses is not "legitimate" in the sense that you and I know it. rather, they are looking at whether the organization represents "adherents" of a religious organization and whether they hae any people in the military. Under the "free exercise" provisions, people that are adherents to a religious group have the right to participate in the religious activities of that group, whether you and I agree with its legitimacy. If this were not the case, the Supreme Court ruled back in the 80's that no one has the right to the "free exercise" of religion if all do not have the right to the "free exercise" of religion. There are many groups represented, even by chaplains, that I had a hard time accepting when I was on active duty as a chaplain: Buddhists, Christian Scientists, Mormons, etc. But, I could not pick and chose who had the right to worship in their own way, and who did not.
Hope that helps a bit.