Okay, there are actually three sides here: the side that thinks religion and science can be compatible, the side that thinks science shows religion to be false, and the side that thinks religion shows science to be false. I spend too much time arguing against creationism, so I’m going to ignore them.
The important issue that those who beat religion with a scientific stick usually fail to address is this:
Religion derives little of its importance from its truth claims. It is powerful because it provides identity, community and meaning.
And none of those three rely on the truth claims for their potency, except meaning, and even then I’d argue it is a minor thing.
If all churches in the world, tomorrow, admitted that their doctrines were not empirical. They all renounced all their claims for God’s detectable intervention in the cosmos. In short if they conceded that science and religion were incompatible and science won. Membership would drop undoubtedly. But I suspect it would not be decimated. Most catholics would still be catholics, most anglicans still anglicans, most orthodox still orthodox. Most people would modify their beliefs and not lose their faith, and some may come into the church as a result.
I know quite a few Christians who’s beliefs are indistinguishable from mine. They are Christians. Why? Because they chose that to be their identity, they chose that community to be their community, they choose that mythology to be the lens through which to see meaning in the world.
And that’s why, when non-compatibility folks launch into a devastating dismantling of Christian truth claims, most Christians don’t give a fig. In fact most Christians who are professional scientists don’t give a damn.
I’ve heard Richard Dawkins describe this with obvious frustration as a compartmentalizing in religious scientists. They simply won’t let themselves look at their religion with the same eyes they do their science. It doesn’t surprise me. Most scientists don’t look at most things in their life that way. It would make for a shakey marriage, for example. No, religious folks understand, by and large, that while empirical claims may be part of the machinery of religion. That’s not what religion is really for. At least that’s not what they use it for. So all the scientific and logical arguments in the world will sail irrelevantly by most believers.
The real question is, and one I’d love to find the answer to, can we bootstrap the same power of identity, community, and meaning, from where we are now in our western culture, without the doctrines of religion? Can we figure out how religion works its magic, not to dismantle that magic (because people need identity, community and meaning), but to replace it with something that has fewer negative side-effects? That question is empirical, and would take some really interesting work in social science to answer. That is a science vs religion conversation worth having.