Opinion by Chris Stedman, special to CNN

(CNN) – Conservative atheist and television pundit S.E. Cupp has come out swinging against progressive atheists.

In a clip (see above) for CNN’s “Crossfire,” she argues that conservative atheists are “better” than liberal nonbelievers. What’s more, Cupp says, those on the right respect and tolerate atheists more than liberals do.

She’s wrong, and here are three reasons why.

Fact: Atheists are still political outcasts.

“It seems like there’s this idea perpetuated by atheists that atheists are somehow disenfranchised or left out of the political process,” Cupp says. “I just don’t find that to be the case.”

Survey data contradict Cupp.

For instance, a 2014 Pew Research study found that Americans are less likely to vote for an atheist presidential candidate than any other survey category—even if they share that candidate’s political views.

Faring better than atheists: candidates who have engaged in extramarital affairs and those with zero political experience.

And unless she recently had a change of heart, Cupp herself falls in line with the majority of Americans. In 2012 she said, “I would never vote for an atheist president. Ever.”

While atheists are making political inroads, we’re also still on the margins in a number of ways. Cupp concludes the clip by saying, “I think our atheists are better than yours.”

Apparently they’re still not good enough to be president.

Fact: Conservatives are hostile toward atheists.

“There’s another myth: that conservatism is somehow hostile to atheism,” Cupp says. “I’m a conservative atheist (and) I’ve felt very welcomed.”

But Cupp goes beyond arguing that conservatives broadly welcome nontheists—she also argues that liberals are less accepting of atheists.

“I’d go so far as to say conservatism is far more intellectually honest and respectful of atheism than liberalism has been,” she says.

Again, Pew’s surveys suggest otherwise.

While the number of people who say they wouldn't vote for an atheist candidate sits at 70% among Republicans, that number drops to 42% among Democrats. (“Progressive,” “liberal,” and “Democrat” certainly aren’t synonyms, but there is overlap.)

Of course, conservative hostility toward atheists goes beyond voting for a presidential candidate.

Earlier this year, the group American Atheists announced plans to sponsor a table at CPAC, the country’s largest annual gathering of conservatives. But within hours, after a number of conservatives spoke out against their inclusion, they were promptly uninvited.

Many of the most prominent anti-atheist voices—including Sarah Palin, Erick Erickson, Mike Huckabee and Newt Gingrich—are conservative politicians and commentators, and I have yet to hear many other conservatives (Cupp included) condemn their anti-atheist remarks.

On the other hand, a number of political moderates and liberals have welcomed nontheists.

In 2009, for example, President Barack Obama became the first commander in chief to reference nonbelievers in an inaugural address. The next year, his administration became the first to meet with representatives from the atheist community.

Overall, a much larger percentage of the religiously unaffiliated (a category that includes many atheists) identify as liberal than conservative.

In 2012, Pew reported that 61 percent of nonreligious Americans are either Democrat or lean Democrat, while just 27 percent identify as or lean Republican.

If it truly were the case that conservatives are much more “respectful of atheism,” I would expect to see more Republican atheists.

Fact: Most liberals respect religious diversity.

“Conservatives appreciate an intellectual diversity,” Cupp says. “In contrast, on the left it seems as though there is this knee-jerk embrace of what is more like a militant hostility to faith.”

If you’ve been paying attention to Cupp’s arguments so far, this one should be a bit confusing. Which is it? Are liberals hostile toward atheists—or the religious? (Or are liberals just hostile toward everyone?)

But religious diversity is actually significantly greater among Democrats—for example, Pew reported in 2011 that just 11% of Muslims affiliate with Republicans, while 60% identify as or lean Democrat.

By contrast, as much as 74% of GOP voters identify as Christian, according to recent surveys and polls.

Finally, Cupp lifts up self-identified progressive Bill Maher—who has said, among other things, that religious believers have a “neurological disorder”—as an example of liberal intolerance.

I should give credit where it’s due: Cupp is partially right here. Maher’s take on religion is problematic and should be condemned.

But his views certainly aren’t representative of most of the progressive atheists I know. Suggesting that Maher speaks for atheism is like saying Pat Robertson represents all of Christianity.

In the end, I’m not arguing that progressives are perfect. We have plenty of our own issues and aren’t as welcoming of atheists or some believers as we could be.

But to say that we’re less tolerant of religious and nonreligious diversity than conservatives? Well, that’s just hard to believe.

Chris Stedman is Executive Director of the Yale Humanist Community, author of "Faitheist," and atheist columnist for Religion News Service. Follow him on Twitter @ChrisDStedman. The views expressed in this column belong to Stedman.