What do Donald Trump, Hillary Clinton and Mark Zuckerberg have in common? They all profess to be religious. As a new study shows, people think the worst of non-believers. What does this mean for US voters?

The notion that Facebook founder Mark Zuckerberg is considering a run for president in 2020 seemed fanciful until the final days of last year, when he posted a message (on Facebook, naturally) that read: “Merry Christmas and Happy Hanukkah from Priscilla, Max, Beast and me,” referring to his wife, his daughter and his dog. A generic festive message from a CEO, you might think. But then a commenter reminded Zuckerberg that he had long identified as an atheist. What had changed? The answer was swift: “I was raised Jewish and then I went through a period where I questioned things, but now I believe religion is very important.”

This statement, more even than his proposed voyage around all 50 states or his much-hailed visits to key, first-in-the-nation states such as Iowa, suggested that the tech wizard was eyeing the White House. For Zuckerberg was tacitly acknowledging one of the golden rules of US politics: Americans won’t vote for an atheist for president.

That maxim has been reinforced by a new study, which shows that people across the world are prepared to think the worst of atheists, believing that those without faith are more capable of immoral behaviour than those who have it.

The man behind the study, Will Gervais of the University of Kentucky, told the Times he had been prompted to research the topic by data that suggested US voters are less willing to elect an atheist than any other category of candidate, including gay or Muslim. Gervais said he suspects that voters consider belief in God essential for morality and deem atheists “moral wildcards” who lack restraint and are capable of anything, including “kicking puppies, cheating at cards, light cannibalism”.

US political operatives have long worked on this assumption. Witness the leaked Democratic party documents that showed allies of Hillary Clinton in 2016 considering a plan to paint Bernie Sanders as an atheist, believing it could cost him crucial percentage points in God-fearing states such as Kentucky and West Virginia. Sanders, who is Jewish, rushed to assert that he was no atheist.

This means that no openly non-believing candidate has won the presidential nomination of either major party. Even figures whose personal morality has been famously suspect have rushed to assert their affinity for God. The most egregious example is surely the current incumbent of the White House. Despite leading a life dedicated to the worship of mammon, Donald Trump was embraced by white evangelical voters, who accepted his declarations of devotion and saw him as preferable to church-going Clinton. It suggests that, while Americans expect their politicians to profess faith in God, they hardly demand consistency.