USA Today article don't prove it. The main argument seems to be that religion uses different methods to arrive at claims about events that also come under the purview of science: "wonder-working saints and divine cures, virgin births, annunciations and resurrections." Right, but then art critics make claims about entities and events that also come under the purview of science: like paintings and performances And the methods of art critics are completely different from the methods of science.
What I suppose he meant to say is that the findings of science flat out contradict the findings of religion, and that there's a reason why science must be considered right every time. Not every time but a few, but every single time. I imagine his USA Today readers might like to know why that should be so.
Then there's the curious inconsistency about the use of examples. How can it make sense to scoff at using religious scientists as evidence of religion-science compatibility, but then write "don't just take my word for the incompatibility of science and faith — it's amply demonstrated by the high rate of atheism among scientists"? Either Francis Collins is evidence of compatibility and the atheist scientists evidence of incompatibility, or none of them have any evidential force. Coyne says citing Collins is like using cases of marital infidelity to show that monogamy and adultery are compatible. But if so, it's just as pointless to use instances of marital fidelity to show that monogamy and adultery are incompatible.
Then again, the analogy isn't actually so good, because monogamy and adultery are incompatible "analytically"--it's just a matter of meaning. But science and religion aren't incompatible just as a matter of meaning. It's harder to say what the truth is. Citing religious and atheist scientists is at least mildly probative...in both cases. It's basically an appeal to authority. The religious scientists presumably say: compatible. The atheist scientists say: incompatible.
But only mildly probative. Some religious scientists probably see a tension between religion and science. They may not have sorted out how the two things fit together. And atheist scientists don't have to see a tension between religion and science--they may reject religion just because they don't believe it. Scientists are Democrats, by a huge majority, but that doesn't mean they think science is incompatible with Republican politics.
So: case not closed. I don't think Coyne's arguments really ought to convince religious readers of USA Today (which means most readers) that they have to make a choice between religion and science. And it's a good thing too, because if presented with that choice, I think most would choose religion.