His past veracity is never going to come up. It’s irrelevant, unless he can be shown to have lied in a criminal way—i.e., to be an actual perjurer.
The case will be decided on the basis of religious freedom, and his case is airtight, because religious liberty protects his option to be an atheist.
The bottom line is that yes, he will win the case, but the question is at what cost? A win should be more precious if it comes at great cost. One would hope that this win will be very precious to this joker!
An illustration: About 20-25 years ago, a Vancouver Sikh was accepted into the RCMP Academy. After passing, he decided that his religion required him to wear a turban rather than the RCMP Stetson. It went to court and he won. His first assignment was in the NWT. (This is not unusual as newly minted Mounties are posted far from home and usually in the North.) What he discovered was that the NWT First Nations had no respect for a Mountie who wore a turban, rather than a Stetson. He was beaten by many First Nations people and when he would call for backup, unfortunately somehow, his fellow Mounties were rarely able to respond quickly. Eventually, he quit the Mounties and joined the Vancouver Police Service. Funny thing though, he was seen in public on occasion, not wearing his turban, the one that prevented him from wearing a Stetson!
That atheist in the USAF, may find ‘karma’, as he may call it, is not a nice thing. As for me, I know that God will not be mocked.