If Gopnik had found proof that Hume showed an interest in Buddhism or that it was ever mentioned to him at La Flèche her research might be of some value. As it is it’s irrelevant, I think, because it’s not all that unlikely that Hume could have found out about Buddhism anyway, from other sources, if he were at all interested. There is, of course, a vast historical chasm between could have and did. As one of the West’s leading sceptics and the author of some of the most slyly biting sarcasm about religious beliefs it isn’t particularly likely Hume would have sought to learn from Eastern religions, but let it pass; for the sake of argument we can grant that he might have heard the gist of Buddhist doctrine.
One of the problems with this criticism is that it floats quite free of the actual evidence, whereas Gopnik's argument, while tenuous, does not. In history of philosophy we do not say "it’s not all that unlikely that Hume could have found out about Buddhism anyway, from other sources" unless we have evidence of such sources at least being possibly available; in fact, as Gopnik herself has pointed out, there were very few such sources in the early eighteenth century when Hume was writing the Treatise, and almost all of them Jesuit. Likewise, the comment about religion looks suspiciously like setting up an imaginative profile of Hume and then assuming, without regard for the evidence, that the historical Hume complies with it. In fact, there is extensive evidence of Hume reading religious works and discussing religious topics during his period of writing the Treatise. We know, for instance, that he read quite a bit about the Jansenist controversy, and that he had read works in Catholic spiritual theology (almost certainly Fenelon, and likely a few others), and that he had a good knowledge of Protestant anti-Catholic polemic; and (as Gopnik notes) we have evidence directly from Hume himself that he discussed philosophical matters with Jesuits in this period. Likewise, the later Natural History of Religion attests to Hume's interest in the diversity of religions. Thus there's no particular reason to think that Hume wouldn't have been interested in tales of a religion so different from Christianity; to the contrary, actually.
It is true that there is a chasm between could have and did. But there is also a chasm between abstract possibilities or even expectations on one side and possibilities that arise given the actual evidence on the other. It is of interest to know whether parallels or analogies are artifacts of interpretation, coincidental similarities, convergent developments, or connected by cause and effect, and how one goes about interpreting them depends quite crucially on what evidence one has one way or another. Given Gopnik's research, it is still quite likely that any parallels would be at most convergent developments, and the simplest interpretations of the arguments even given the evidence are still those that make that supposition. (The post notes that it can be put in the context of a response to Descartes -- which is true enough, although it would probably be in response to Cartesians generally; but it is also true that Hume's actual argument shares a number of structural points with some of Berkeley's attacks on matter -- they both make use of the impossibility of perceiving how things exist without perception, for instance.) But identifying a possible channel of influence is non-trivial progress; far from being irrelevant, it raises further questions for research and inquiry, since the kinds of channels of influence that are available can make a significant difference on how the influence itself would actually work and on the range of interpretations available for the argument in question. And Gopnik herself, it should be pointed out does not claim to have established more than a real evidential possibility of a contributory cause.
There is another aspect of the criticism that is not outright stated but seems to be implied; at one point the post seems to suggest that, without assuming the hypothesis that Hume just forgot the source of the ideas, Gopnik's claim would suggest that "Hume, the most honest and modest of men" had engaged in "dishonesty or culpable silence over his sources". If this is intended, it is not in fact an issue, since it is based on false assumptions about how philosophers and scholars handled sources in the eighteenth century. One can go through Hume's works and pick out regular cases where he has to be following Malebranche, or Bayle, or Locke, or Berkeley, despite his not actually saying so. Arguments in Enquiry Section VII, for instance, are regularly drawn directly from Malebranche, despite the fact that Malebranche is only mentioned by name in a footnote that is only making a general historical comment and does not identify him as a source. And it is even more rare to find citation of sources where the source is a conversation. (In fact, it is still so, despite the fact that conversation must be a very significant source of philosophical ideas both then and now.) There is nothing dishonest or culpably silent about it.
I am somewhat puzzled, incidentally, by this part of the criticism:
That is the real killer for me; Hume did not, in fact, say that the self was an illusion; he saw nothing. On this he may well be unique; he is surely original. Buddhists, and some modern philosophers, contend that the self is actually an illusion; a powerful one which it is hard to shake off, but one which is ultimately misleading. Hume, on the contrary, just saw no self.
What's puzzling is that Hume goes on in the same section to address the question of what gives us "so great a propension to ascribe identity to these successive perceptions, and to suppose ourselves possessed of an invariable and uninterrupted existence thro' the whole course of our lives". Given that this ascription is quite clearly described as a mistake and our propensity to make it is clearly said to be great, and given that one of the points Hume needs to explain is why so many other philosophers don't see the self as he does, 'illusion' seems a good word for it.