Law professor Jonathan Turley has this post on a U.S. Air Force airman who is being denied reenlistment unless he includes in his sworn oath, so help me God. The unnamed airman is an atheist and doesnt want to do that. Of course, the First Amendment to the U.S. Constitution protects his right to practice any religion he wants, as well as not practice any religion at all. And that includes the right to not be compelled by the government to proclaim any belief in God, which obviously is a religious belief.
Now, if he were applying for a job at a privately owned business, then the business owner has a right to require the applicant or new employee to recite whatever words the employer requires. If the applicant or employee doesnt like it, then he can go work somewhere else. That is a matter of private property rights, the right of the business owner to establish ones own rules for ones own business. But this is government employment we are talking about. Since the government is publicly owned, owned by everyone, then this government employer does not have the constitutional right to require a serviceman to proclaim any kind of religious loyalty. Such a requirement should also be considered as establishing religion, which is forbidden by the Constitution. A belief in God is a religious belief.
Bottom line: because the U.S. military is a death machine against innocent foreigners, an apparatus of provocations of foreigners which do nothing but make the American people more vulnerable, unsafe, and less secure, then no one should be joining this criminal organization, period.