I'm no fan of NOMA myself. For one thing, NOMA is an utterly vague claim about an utterly vague supposed distinction between two vague fields of human endeavor -- although it's often a little vague whether these fields are primarily practices or bodies of belief. But I don't think Kuznicki's argument is the way to go. For instance, the notion that there was ever a "western religious synthesis" (as he puts it later in the post) of which the design argument was an "integral part" is absurd. (And which design argument? As Darwin himself points out in one of his letters, he himself could think of three completely different design arguments that were biological in one way or another. He wasn't persuaded by any of the three, but only one was affected by the theory of natural selection.) For one thing, it's absurd to say that there has ever been a "western religious synthesis"; for another, it is absurd to say that the past century-and-a-half has seen its consolidation. Design arguments for God's existence played very little role in Christian thought for 1700 years; for
Further, I don't think Kuznicki's post ends up being very consistent in the end. His original point is that NOMA is wrong because religion rests on empirical foundations; and then undermines this argument by denying that it does if it uses cosmological arguments, moral arguments, and fideism. (I note, incidentally, that Kuznicki assumes that 'religion' and 'theism' are coextensive. I'm OK with this assumption, since I think it's a useful way to use the term 'religion' without being vague, but it's not one most people would accept.)
Nor do I think Kuznicki's line of argument even has the potential of having a serious effect on NOMA views, for the simple reason that he doesn't address the core claim of NOMA. The core claim is not that no one ever confuses religious and scientific claims, but that science and religion each have a legitimate 'magisterium'; each has a rationally legitimate function -- science deals with facts, and religion with values. Thus, if a NOMA proponent says that the Bridgewater Treatises are an illegitimate expression of religion (or science), he is not engaging (as Kuznicki suggests) in True-Scotsmanship, because he is not re-defining the term 'religion' but diagnosing a mistake. The point is not that the term 'religion' needs to be redefined to exclude the Bridgewater Treatises, but that the Bridgewater Treatises commit a category mistake by conflating two different rational functions and bodies of thought. It is as if one were to confuse trigonometry with romance. If someone did, or even if it were common, it would not be unreasonable for someone to say that there are two rational functions being confused here that need to be distinguished. (One could, perhaps, argue that the growth of astronomy out of astrology, or chemistry out of alchemy, involved precisely this sort of diagnosis and distinction, e.g., alchemy confuses the rational functions pertaining to fact and value, and so tries to be both a chemical explanation of the world and a spiritual quest in one.)
Now, I think it's fairly clear that NOMA is just not a tenable position for discussing the relation between science and religion, however one conceives those. As I said above, it's really a vague mush. And, however it might seem on first impression, it's not irenic at all, but guaranteed to annoy everyone all around. NOMA would, strictly speaking, require scientists to defer on all points of ethics -- not a minor issue given the importance of keeping research ethical -- to religious experts; it would require religious experts never to talk about facts within their field. There has never been a good argument for either of these. If you are genuinely tempted by NOMA, you should be a Kantian instead; the Kantian view is probably the closest serious view to a NOMA view, and is much more rigorously argued than anything NOMA advocates have.