To be fair, the military doesn't want to accept people who would disobey a direct order over something so petty. If they aren't mature enough to say "so help me God" and move on, they don't want them.
Insisting that the federal government obey by the Constitution is petty? For the government to enforce any religion on any level is strictly forbidden and the interpretation is even broader than that. It's the very first thing in the Bill of Rights.
