An atheist for President?

[Orser67]

As reasonable of a shot as any other category of person that is only ~5% of the population.

I disagree that it's as simple as that; as OP states, there's an unusually high number of people who wouldn't vote for an atheist for president. E.g., comparing to other groups that represent a single digit percentage of the population, 538 shows that people are more likely to say that they wouldn't vote for an atheist than for someone who is Jewish, Muslim, or gay. In fact, the only group that's more unpopular than atheists in the poll are socialists.

[Orser67]

I think a self-described agnostic or otherwise irreligious person would have a solid chance of winning the Democratic nomination so long as they were respectful of other peoples' faith (though they'd have a tough time forming the right combination of voters). They'd probably suffer an electoral penalty in the general election, but it would probably only be 1-2% at most. I don't think they could win the Republican nomination, though.

A self-described atheist in the style of Sam Harris or Richard Dawkins might have a shot at the Democratic nomination, but they'd get blown out in the general.

[Orser67]

I thought this article/poll was interesting and relevant to the topic. Essentially, evangelicals are less tolerant of atheists/agnostics than vice versa:

...respondents were asked whether their selected group should be allowed to give speeches in the community, teach in public schools, run for public office and other liberties. Americans are not particularly tolerant of groups they dislike. Only 30 percent are willing to allow their disliked group three or more such activities.

But 65 percent of atheists and 53 percent of Democrats who listed Christian fundamentalists as their least-liked group are willing to allow them to engage in three or more of these activities. That’s a much higher proportion with tolerance than the sample overall.

...a smaller proportion of white evangelicals would behave with tolerance toward atheists than the proportion of atheists who would behave with tolerance toward them. Thirteen percent of white evangelical Protestants selected atheists as their least-liked group. Of those, 32 percent are willing to extend three or more of these rights to atheists. In fact, when we looked at all religious groups, atheists and agnostics were the most likely to extend rights to the groups they least liked.