It seems to me that there are a couple of different conceptions of religion, and that the conversations between New Atheists and those more sympathetic to religion are difficult because they’re both working with different conceptions and talking past each other as a result. This difference in approaches is something that Jonathan Haidt points to in The Righteous Mind, and the following is inspired by that book, though very much filtered through my own ways of thinking about it.
The New Atheist conception of religion is that it is primarily a set of beliefs. In particular, it is a set of beliefs with claims about the supernatural, the origins of life, and morality. These claims can be either true or false. They are valuable to the extent that they are true, and they are trustworthy to the extent that they can be verified independently. This is the view of religion that I grew up with.
More recently, though, I have started to see an alternative conception of religion. In this conception, religion is valuable to the extent that it enables cooperation, and trustworthy in proportion to the length of time in which it has survived as a tradition. This sounds strange to say, and I’m not sure that I’ve articulated it entirely correctly, but that’s because I’m trying to put into words something that is more often left implicit. People don’t say that they value their religion because it enables cooperation – they would say that they value it because it’s right. But religions have emerged through an evolutionary process. You wouldn’t say that you’re attracted to someone because they would impart good genes to your offspring, but that’s what’s going on behind the scenes. Similarly, cooperation and the benefits that come from that are the means by which a religion thrives. As for being trustworthy merely by virtue of being long-lived, on the other hand, that’s a fairly common heuristic. You can see it any time anyone makes an appeal to tradition.
There are a bunch of cultural innovations that enable us to coordinate more smoothly. Some are codified in religion, some not. A few examples off the top of my head: money allows us to keep track of who owes what to whom; conventions about which side of the road to drive on prevent us from crashing cars; both democracy and hereditary monarchy are mechanisms that remove doubt (and thus conflict) about who is in charge. Some of those coordination technologies are clearly better than others, some are debatable, and some, like which side of the road to drive on, are indifferent and the important thing is just that everyone agrees.
According to the New Atheists, the inaccuracy of religious beliefs is a major downside to the religion. But according to this view in which religion is a coordination technology (for want of a better term), the specific claims of the religion are less important than the behaviours that it enables. Religious societies seem to have higher levels of trust than non-religious or mixed religion societies. In particular, people of a particular religion trust other people of that same religion. This allows them to, for example, trade with each other using some shared ground rules and a shared authority to which they can appeal if something goes wrong.
Furthermore, if you want to have a shared set of moral principles, it’s not enough to simply agree on those principles. You also need some way of communicating those principles through time to your descendants. So a sort of meta-coordination technology, then, is to gather every week and re-affirm those principles with the rest of the group. If you only see religion as being a set of beliefs, then you’re likely to be confused by the importance of regularly practising a set of rituals. But it makes more sense if you see those rituals as the process by which the set of beliefs is maintained over generations. And notably they remind themselves of this moral code together so that there can be no doubt about whether they all share it, which might be a mechanism to avoid defections in prisoners’ dilemma situations.
So I think that if you’re seeing religion purely in terms of whether it’s true or not, and if you’re not counting the benefits that come from trusting that the people you encounter will share your moral system, then you’re likely to misunderstand the concerns of people who wish to defend religion against atheism.