Here is what Jerry Coyne said:
I wouldn't entrust political power to someone who believes that while professing religious belief, declaring fealty to the Bill of Rights and the Universal Declaration of Human Rights . The idea that there is some constitutional requirement to vote for someone who believes that kind stuff is one of the nuttier superstitions current in contemporary pop-liberalism.
And it's certainly not just Jerry Coyne who believes that we are meat automatons programmed by physical laws -almost always by "our genes" these days - that is an increasingly common belief in the general culture, one which comes directly from scientistic materialism, which is a deterministic ideology. Here is another of the heroes of contemporary atheism, Richard Dawkins, on the topic:
In a universe of electrons and selfish genes, blind physical forces and genetic replication, some people are going to get hurt, other people are going to get lucky, and you won't find any rhyme or reason in it, nor any justice. The universe that we observe has precisely the properties we should expect if there is, at bottom, no design, no purpose, no evil, no good, nothing but pitiless indifference.
There is nothing in materialism that can overcome that determinism* which is so at variance with the experience of most people. There is nothing in the ultimate reality of materialists that can overcome the assertion of that view of life. There is no reason for anyone to believe that a materialist who believes there is "no evil, no good" will reliably tell the truth, refrain from stealing, or killing or committing any other crime that they think they can get away with. The fear of not getting away with it has proven to be quite ineffective in promoting good behavior and beneficial government, especially among the powerful and wealthy. If you heard a politician say that they belived there is no such a thing as good or evil, but that a god of "pitiless indifference" governed the universe and, furthermore, that the ones chosen by that god to be "lucky" just plain win, you would be insane to vote for them. Yet that kind of thing, replacing physical forces for god, is regularly said by atheists to, at most, muted objection by other atheists or even religious liberals.
If you don't believe that there is moral obligation in life that requires people not be hurt and exploited by those who are "lucky" or those who aspire to be "lucky", through that kind of exploitation if you don't believe that there is moral obligation that not only supersedes the far more destructive passively indifferent observation of intentional harm and exploitation, there is no amount of merely expressed good intention that anyone should believe will result in anything but harm and exploitation. The results of believing in materialism will always devolve, at best, into something like a putrid social Darwinism because there is nothing to stop that. The government and culture of Victorian Britain was an experiment in the ability of mere stated good intentions, cultural preference and habit based in religious professions, to overcome similar assumptions and it was a disaster for the large majority of people. And that is the best possible outcome. Atheist governments since the late 18th century have uniformly been an actualization of the amoral assertions of materialists where the only guarantor of being spared from brutality is mere chance.
If an atheist wanted me to vote for them they would have to explain to me how they account for all of those things that are the moral foundations of democratic government which are denied by contemporary materialism. Due to the record of those kinds of assertions by the heroes of atheism and the horrific record of what happens when atheists take hold of governments, it is entirely rational for a voter to demand assurance from an atheist before they vote for them. I have knowingly voted for atheists twice, in my memory, based on my knowing them and knowing that their atheism was not based in any kind of firm ideological position such as materialism. I don't think I'll continue to vote for atheists on that basis of trust now that this kind of materialist undermining of democracy has gained currency among atheists.
As I've said for years now, the "no religious test" of the constitution is binding on the legislative, executive and judicial branches of the government and the agencies of the government, they are not and have never been binding on individual voters or even groups of voters. Individual voters are perfectly free to consider the religious and ideological beliefs of people who ask for the privileges of having their vote and their permission to assume power. There is no right for anyone but the winner of an election to assume an elective office. And it would be far better if that was looked on as a privilege and a responsibility than as a right.
I have every confidence that if you asked them, a huge majority of atheists and most professed liberals would say they would not vote for a biblical fundamentalist, something which is certainly as much a "religious test" as not voting for atheists. I would tend to doubt I'd vote for a biblical fundamentalist for similar reasons to those that now make me skeptical of voting for materialists. Of course, if you believe that equality is also a delusion you wouldn't be troubled by a failure to act evenhandedly. Which is a definitive example of the fact that when you look at the problems that materialism causes for liberalism, those are fundamental, inescapable and pernicious. There are many ideologies that rationally prevent a liberal voting for a person holding that ideology. And, more importantly, there are moral reasons to not vote for them as well.
Ironically, if you believe what Coyne and Dawkins say, there is no moral or rational basis for atheists to complain about their unequal treatment by voters. The very complaints of unequal treatment that atheists make are undermined by their own materialist determinism. In a morally indifferent universe, atheists have no right to equal treatment, no one does. "Meat automatons" have no rights that anyone is morally obliged to recognize, which is the fatal blow to liberalism which is inherently a part of materialism. People who declare themselves to be nothing more than that have no rational basis for asserting their right to other peoples' votes. It would be foolish to vote for people with such poor reasoning ability as to not see that discrepancy.
The current ideology of atheism is a huge obstacle to believing that democracy is a valid form of government or even possible. I say that due to things which atheists, themselves, say, atheists like Coyne and Dawkins who have large followings among atheists. That some of them try to back track and come up with patch jobs to try to make their materialist ideology tolerable for the majority who believe that human history and experience are more effective proof that democracy is the only legitimate form of government doesn't change that. I have yet to see one of those patches that didn't fall off at first washing. Far from being an expression of bigotry, the decision to not vote for an atheist, in the absence of a convincing refutation of determinism and amorality, is an entirely rational decision.
* I've heard Daniel Dennett come up with some pretty absurd stuff which manipulates this problem by redefining free will into scenarios of mere indeterminacy, something that hardly meets either the concept of free will or its efficacy to produce effectively beneficial government, the goal of democracy. I'm not impressed enough with Dennett's arguments to want to go into them. I think they are shallow, unserious word juggling. I might change my mind and go into them later.