Looks like they are hiding behind the letter of the law as written by Congress.
He has until this time to complete the Department of Defense Form 4 in compliance with the Title 10 USC 502.
Were the US Constitution honored much anymore I might refer to something about no religious tests as mentioned in Article VI:
The Senators and Representatives before mentioned, and the Members of the several State Legislatures, and all executive and judicial Officers, both of the United States and of the several States, shall be bound by Oath or Affirmation, to support this Constitution; but no religious test shall ever be required as a qualification to any office or public trust under the United States.
(Bold face mine in both quotes)
Since the COTUS has been used as toilet paper, we are now a nation of men rather than laws, and folks seem to be dividing up along lines they see fit, I am at a loss to wonder why atheists ought to be spared the effects of the Great Sorting?
Sure, this airman has a great case if the COTUS means what is says & is valid, but who reads the COTUS anymore and applies it as written?