I think it's fair to say that Coyne is firmly in the anti-accommodationist camp. He wrote the New Republic article to review books by Kenneth Miller and Karl Giberson that attempt to reconcile religion and science. Miller, and Giberson, both scientists, believe that religion and evolution are compatible, that is, they belong to the accommodationist camp. Being religious and scientists this would be inevitable, though many accommodationists are atheists, just not of the new variety.
Coyne's article covers the political and philosophical aspects of the debate. The political aspect is concerned with how to change the fact that many Americans do not accept the science of evolutionary theory because it conflicts with their specific religious beliefs. This means the political dispute arises from the philosophical. As I've stated before the so called new atheists, and thus anti-accommodationists, are loud and proud, or strident and shrill depending on your own vantage point. For them attacking creationism with science and rationality is par for the course. This rankles many. According to Coyne, for some accommodationists at least, the fault then lies at the feet of the new atheists. If only the uppity atheists would tip-toe around the thorny issue of compatibility so that the faithful would have no problem reconciling their beliefs and evolution.
So the obstacle to understanding is not religion, it is those aggressive atheistevolutionists who won't shut up.
If this statement is accurate then there is a denial of free speech here and an unsupported assertion that the rejection of evolutionary theory has accompanied the recent phenomenon of atheists asserting their message and challenging religious hegemony. It is easy to see that this would upset the anti-accommodationists and that they couldn't endorse a policy based upon it. One could be snarky here and suggest that given that evolution has been rejected by some segments of the religious for many decades and new atheism is so recent then perhaps it's an example of reverse causation.
It is reported that the National Academy of Sciences (NAS) supports a broadly accommodationist stance as it has a statement that
Many scientists have written eloquently about how their scientific studies of biological evolution have enhanced rather than lessened their religious faith.
but not mentioning that many scientists do not find specific religious beliefs and evolution compatible. This is problematic because the anti-accommodationists feel that the body should take no political position on the issue and solely focus on advancing science. It should not be partisan. It follows then that they would not endorse the NAS supporting any anti-accommodationist stance either.
On the philosophical side the article raises different versions of compatibility in dispute; first psychological compatibility,
there are religious scientists and Darwinian churchgoers. But this does not mean that faith and science are compatible, except in the trivial sense that both attitudes can be simultaneously embraced by a single human mind
and epistemic incompatibility,
[t]he real question is whether there is a philosophical incompatibility between religion and science. Does the empirical nature of science contradict the revelatory nature of faith?
Coyne continues by arguing that one way to make science and religion compatible in an epistemic sense is to redefine one to be encompassed by the other. If by religion we mean pantheism, identifying nature with god, then there is no incompatibility between science and religion for example. This point is important because there are versions of religious beliefs that are or can be made philosophically compatible with scientific knowledge. Philosopher's gods, such as deistic or ground of all being deities seem compatible with science, at least they don't contradict the knowledge derived from science specifically because they make no claims to knowledge about the observable. But these deities have lost their personal nature and thus what makes them appealing to many believers. Why pray to an indifferent force or entity? My previous post stated that epistemic incompatibility was between science and religion. But that was so indefinite as to be wrong. It is between the knowledge we derived from science and specific religious claims that incompatibility arises. A question then is whether believers are happy to alter or give up any beliefs that are incompatible with scientific knowledge. Young Earth creationists reject evolutionary theory because it directly conflicts with their beliefs about the origin of humans and the age of the Earth.
Coyne offers some more examples of somewhat procrustean attempts to make science and religious claims compatible and in the end, which is not surprising for an anti-accommodationist, finds them unsatisfactory.
I recommend reading the article as I believe Coyne shows none of the stridency or shrillness often attributed (mostly falsely in my opinion) to the new atheists while still disagreeing with Miller and Giberson. Again I'd just like to point out the above is my understanding of the issues and whilst I'm biased I hope I haven't seriously misrepresented anybody. If I have please feel free to point this out in the comments.