A Sunday morning in church is not in the cards for those who say they're "beyond belief" -- beyond belief in the God of Scripture, anyway. And for some, the abandonment of their faith wasn't easy. Our Cover Story now from Mo Rocca:

Visit Jackson, Mississippi, and you can't miss the First Baptist Church. To Neil Carter, it was like a second home.

"This is where I grew up," he told Rocca. "My parents were married here. My sisters were both married here. I got baptized here, twice actually."

At the age of 15, Carter says he was "saved" by a youth evangelist.

"It was a very emotional experience for me," he said. "I really broke down into tears. Almost immediately after I got saved, I began teaching Sunday school. And I did that for about 10 years."

After college, he went to seminary, and thought about becoming a minister. But he started having doubts.

"I like to say that I've always lived with an inner skeptic," he said. "Even when I was a kid, I always had a lot of questions that were never really answered."

His questioning lasted for decades. But five years ago, Carter finally admitted to himself that he's an atheist.

It took him another year to tell his wife: "It was very upsetting -- for her, it felt like it was like I had died. The man that she had married was gone."

Their marriage (they have four daughters) ended in 2012.

But Carter says he never mentioned his atheism to his middle school history students.

Rocca asked, "How did the kids find out that you're an atheist?"

"One of them had been stalking me on Facebook and saw that I had 'liked' a page about atheism," Carter said. "And then she came to school the next day and started asking me in front of the students if I was an atheist, and I refused to answer the question, which to them was enough of an answer."

The principal soon instructed him never to discuss anything to do with religion in class. And shortly after, he was transferred. "First, they moved me out of my classroom to a math class," he said. "And then after that, they just told me they wouldn't bring me back the next school year. They didn't really give me any reasons, but obviously I knew what the reason was."

We don't know for certain why Carter was transferred. No reason was documented, and his school declined to talk with CBS News.

Since 2013, he's been teaching math at a nearby high school. He started a blog: Godless in Dixie, and he's joined a group called "Openly Secular."

On its website, Carter talks about the price he says he pays for declaring he's an atheist:

"Because around here, people are taught that morality comes from religion. So if you don't have religious beliefs, then you must not be a moral person."

"Like a light switch, it's, 'You're immoral, you're gonna raise evil children, you're a bad parent,'" said Todd Stiefel, of Raleigh, North Carolina. A former Catholic, he leads the Openly Secular campaign. "They're questioning your whole existence. I'd rather somebody assume I'm stupid than assume I'm wicked. It's painful. It's discrimination. It's prejudice."

Openly Secular is a new effort by 30 organizations and some well-known names (including "Saturday Night Live" alum Julia Sweeney) that asks non-believers to go public. "Yes, I'm an atheist, but it was a really hard word for a lot of people to handle, including, for example, my parents," said Sweeney.

While seven percent of Americans say they don't believe in God, only a little more than 2 percent call themselves atheist.

"The word 'atheism' has really bad branding," said Stiefel. "A lot of people don't want to associate with the word even if they are. I've had people say, 'Oh, I don't believe in God, but I'm not an atheist.' They don't want to use the term because it brings such baggage and hatred."

During the 1960s, the face of atheism was Madalyn Murray O'Hair, who famously crusaded to end mandatory Bible readings in public schools. "I felt that this was an unconstitutional practice in relation to separation of church and state," she'd said.

She was, to say the least, a polarizing figure ("The most hated woman in America," read one headline). Openly Secular is taking a different approach, focusing less on the law and more on the court of public opinion.

"It's about changing hearts and changing minds," said Stiefel. "It's about people realizing that we are somebody you don't need to fear. We're somebody you don't need to distrust."

They've got their work cut out for them. Fifty-three percent of Americans say they'd be less likely to support an atheist for president. In politics, an admission of atheism is virtual suicide.

"They can't get elected in this country," said Stiefel.