science and faith are incompatible: preliminary stuff

So I've been reading Jerry Coyne's first two posts on the problems with science cosying up to religious beliefs. Coyne's first post is a general argument, while his second is a critique of the apparent policy of accommodationism at the National Center for Science Education [NCSE] in the US. I've not found anything to disagree with, and there's much to bolster my own thinking. Clearly the first post is most relevant to me, though the second post does make me wonder whether there are any issues here in Australia, on the equivalent level of the NCSE, which might be worth investigating. For now, though, I'll focus on the general issue.
As I've already pointed out, attempts by Christian believers to reconcile fundamental tenets of their faith - the fallenness of humanity, the existence of the human soul, the specialness of humans as a species 'in God's image' - with scientific understanding, and particularly evolution, have been pretty well disastrous. Even so, these attempts are continually made, which itself is indicative of the belief that science and faith are not 'non-overlapping magisteria' - the pretentious terminology coined by Stephen J Gould. The Christian doctrine of human fallenness is a claim about how the world is for us, not 'metaphorically', but really. All religions, as Coyne points out, make these claims about how the world is, and this is clearly the province of science. Virtually all the flat-earthers of the nineteenth and early twentieth centuries were 'guided' by religion, and of course we have the young earth creationists and other religiously inspired pseudo-scientific groups, all claiming to have science on their side. The Catholic church is constantly fudging on the issue of evolution and human specialness. Its position is essentially incoherent, but it clearly doesn't suffer from the delusion that evolution is irrelevant to the Christian faith.
But I won't belabor the point - religion invokes supernatural stuff to explain aspects of our natural world. Science is all about explaining the natural world, and finds no need for supernatural hypotheses. Clearly they are in opposition to each other.