The battle in the military over the rights of service members who believe in God and those who don’t continued this week with a secular advocacy group asking the Navy chaplain’s office to help overturn the Navy’s recent decision to reject a humanist chaplain.

Jason Heap, a 39-year-old religion teacher and former Protestant youth minister, was told in late May that his application to be a chaplain in the Navy was rejected. Navy officials declined to Heap and to The Post to explain why — citing personnel privacy reasons — but no branches of the U.S. military currently have explicitly nontheistic chaplains.

“As you know well, military chaplains advise on far more than faith and spiritual issues; they handle moral and ethical dilemmas, and enhance morale and unit cohesion,” said a June 10 letter to Rear Adm. Mark Tidd, chief of the U.S. Navy chaplains’ office, from Todd Stiefel, chair of the advocacy group Openly Secular.

Chaplains “often control available meeting space on the base,” said the letter, which was released to the public Tuesday. “If a service member needs bereavement leave to attend a funeral of a loved one at home, the chaplain is the point of contact. Nonreligious service members face the same questions about life and death, fear and loss as any other person in the military.”

Openly Secular was formed in April as an umbrella group for secular movements seeking to combat what they see as discrimination in public places such as schools or the U.S. military. Advocacy groups supporting various nontheistic spiritual movements — including Secular Humanism, Ethical Culture Ethical Union and Humanistic Judaism — have just in recent years become more organized. They are bringing deeper responses to questions about what nontheists believe, what differentiates one group from another and whether they should and will establish the same institutional rights as religious denominations.

While the U.S. military is a more traditional sector of society, the country is going in a few directions when it comes to embracing religious pluralism. Polls show the fastest-growing religious affiliation is “none” — now 20 percent of Americans — yet this week new research found one half of Americans said they’d be unhappy if someone in their family married an atheist.

Groups have been pressing for other services outside just the chaplaincy.

Wiccans in 2007 successfully sued the Department of Veterans Affairs to get the Wiccan symbol — the pentacle — on deceased veterans’ headstones. At the time there were 38 different symbols allowed on military headstones; today there are 57, according to the Military Association of Atheists and Freethinkers, which says the agency “has been a pioneer in recognizing diverse beliefs.”

And this April the U.S. Army added “humanist” as one of the preference codes soldiers can use to identify themselves officially.

According to Association of Atheists and Freethinkers, there are about 4,800 chaplains, none of who are explicitly nontheistic.

Heap, who was born in Texas and grew up in Philadelphia, was a youth minister in the mid-1990s at various Methodist and Baptist churches, according to Jason Torpy, president of the Atheists and Freethinkers group and a West Point graduate who served as a captain in the Army in Iraq in the early 2000s.

Heap then moved away from Christianity and received a Master’s from Oxford University in religious history. He has been teaching religion in various European schools and would not speak for this article beyond a brief statement.

“I am exceptionally disappointed and aggrieved by the Navy’s initial rejection of my application. I will continue to seek acceptance. I hope military leaders will open their hearts to humanists,” the statement said.

Heap has never served in the military.

Torpy says the requirements to provide spiritual care are stacked against nontheists because they require a master’s in divinity and an affiliation with some religious group that would be seen by the federal government as akin to a church.

Meanwhile, some Christian advocacy groups say they are under siege in the military as well. The Chaplain Alliance for Religious Liberty has expressed concern about developments such as the Air Force last fall dropping the requirement that cadets say “So help me God” in their annual oath.

After the Navy’s rejection of Heap, the Alliance praised the decision.

“Chaplains, historically and by definition, are people of faith,” said Ron Crews, the group’s executive director. “You can’t have an ‘atheist chaplain’ any more than you can have a ‘tiny giant’ or a ‘poor millionaire.’ . . . I am grateful that, in this decision, the Navy has honored our long tradition of providing for the spiritual needs of the men and women who serve our nation in the military.”