The inconsistency I refer to in the title of this post appears when Flanagan says that Catholicism is "silly" and possibly "dangerous", but he is willing to give considerable benefit of the doubt to Buddhism and allow it to be judged by its own standards of evidence. My only point in this post is to call attention to the inconsistency and urge similar treatment when the epistemic basis for the two beliefs is roughly equivalent.
Here's Flanagan's summary of the possibility of rational Catholicism:
There is a type of Roman Catholic that can believe in evolution. I perhaps fit this bill: Believe none of the theology or metaphysics. But be a cultural or ethnic Catholic (the way many Jewish atheists are [I assume he means that they are Jewish in only cultural or ethnic but not theological sense, not that they are culturally or ethnically Catholic]). Go to Mass, meditate and pray in a Catholic way if you wish, consult the right saints depending on your needs, have fun, etc. This is a reasonable way of affirming your identity, you can find wise moral guidance in places, and you can drop all the hocus-pocus stuff [God, supernatural creation, immortal souls and God implanting immortal souls in humans]. That stuff is silly, unbecoming to thoughtful souls, and can be dangerous. (p. 105)
On the other hand, Flanagan does not say that the hocus-pocus stuff in Buddhism is silly and potentially dangerous. He does make clear that he disagrees with it, but he does not make this kind of stinging criticism of Buddhism.
I can find a few differences in the belief systems: (1) the Dalai Lama explicitly endorses the epistemic superiority of science over dogma/authority, (2) Buddhism is atheistic, and (3) the moral focus in Buddhism appears less likely to lead to Buddhists harming anyone.
These are all significant differences, but I still think Flanagan is engaged in a bit of special pleading for Buddhism.
(1) The Dalai Lama does say that if Buddhist beliefs conflict with the best scientific evidence, then they must be revised or rejected. However, he also distinguishes disproof of a claim from failure to prove the claim. Let's call this "the caveat". Thus, the Dalai Lama can continue to believe in reincarnation or rebirth and a karmic system of justice for that transcends a single life because there is no scientific disproof of such beliefs only failure to find evidence for them. The problem is that any positive existential claim (a claim that something exists) can make use of this clever distinction. There is no scientific evidence of the Great Pumpkin, the Flying Spaghetti Monster or God or a Christian soul, yet there can be no scientific disproof of their existence either. It is always possible that such a being exists but has simply avoided being seen. Scientists and rational beings in general do not place the burden of proof on those disproving a positive existential claim but on those proving that existential.
Flanagan, on the other hand, says that:
A comprehensive and responsible critique of the doctrine [of rebirth including apparently the caveat about scientific evidence] would need to look at the quality of the inference, which I won't undertake here. (p. 81)
Strangely, he does not call the inference "silly" or possibly "dangerous" but instead passes on evaluating it for now.
The Dalai Lama's belief in science could easily be something that a Roman Catholic might accept were he/she clever enough to do so provided Church authority still held sway in those areas (existence of God, a soul, etc.) in which disproof of the existential claim was impossible. Thus, I do not see Buddhism as coming out significantly ahead of Catholicism in order to distinguish "silly" Catholicism from respectable Buddhism. The Dalai Lama's view does make some improvement on Catholicism because if there were clear scientific evidence of something (say, that Darwinian selection can explain the origin and nature of human life), there would be conflict with religious teaching, and the Buddhist would not deny the claim as the Catholic might. But these differences are quite limited because of the Dalai Lama's caveat.
(2) Obviously, I endorse atheism over theism, so that is a point in favor of Buddhism. But Buddhism does endorse several things--reincarnation, karmic justice, etc.--without evidence, as noted, and so I do not see how this is much reason to prefer Buddhism. In effect, it is as though Buddhism and Catholicism both endorse transcendent justice but only the Catholic explains it in terms of agency, the Buddhist simply takes it as a given. So, both views involve unjustified beliefs in supernatural or transcendent facts. Silly indeed.
(3) That leads to the charge that Catholicism is potentially dangerous. I suppose here the biggest danger from Catholicism comes from accepting its authority over our own scientific evidence or individual reason when it comes to moral claims that potentially could lead us to harm ourselves or others. For example, if a requirement of Catholicism were that we convert the unbeliever no matter the cost, then reason tells us that this is insufficiently tolerant and that we ought not do it. [I really don't know whether this is a consequence of Catholicism; no one much anymore thinks that forced conversion is acceptable.] Are Catholics moral beliefs harmful? Fighting against use of condoms in areas plagued by sexually transmitted diseases is, indeed, very harmful, and Buddhists do not endorse such actions. So the danger from Buddhism is considerably less, especially if our individual rationality can prevent us from acting on Buddhist authority. But it is not clear that science can show us that Catholic is wrong. Perhaps we each individually can reason morally and reject the Catholic teaching. But it may also be that individual reason (as in the case of the caveat above) should trump Buddhist beliefs, yet Buddhism does not endorse this.
However, the moral difference here is more accidental than essential. If Buddhism required conversion of non-Buddhists or did not permit condom use, and since there would be no scientific disproof of these moral principles, it is not entirely clear that Buddhism would not also be dangerous. So, the danger from Buddhism is not evident given its morally very acceptable principles and its nominal respect for scientific knowledge, but the potential for such harm exists given that any role for moral authority. Any religion that gives any place for authority to overcome individual rationality (as the Dalai Lama's caveat above does) and does not conflict with scientific evidence allows for abuse of that authority, whether the authority is currently being abused or not.
Flanagan is inconsistent in that he does not offer the same type of stinging criticism of Buddhism that he does of Catholicism when it appears that the supernatural claims are similar and the evidence for them equally poor. He does make clear that he disagrees with the metaphysical claims about rebirth, souls and transcendent karmic justice. But he refuses to take on the Dalai Lama fully when he dodges the epistemic issue of the rationality of such belief. Worse, when he finally addresses this directly in his appendix (p. 99), he says that Eastern Buddhists (not Buddhists committed to a Western largely scientifically-informed worldview) have their own standards of evaluation and cannot be judged according to Western criteria. After saying that he does not believe in the metaphysical claims of Buddhism, he writes,
But nothing follows from my opinion about what especially non-Western Buddhists ought to believe. I am not sufficiently inside the practice to understand how it works. Buddhism is a noble wisdom tradition with its own internal standards from which it generates its beauty and moral majesty. I think that the belief in rebirth is irrational, but many beliefs are irrational and do no harm, only good. So from where I sit I leave it alone unless it is brought into a discussion of mind science. Then and only then does my opinion count.
My question, then, is why Buddhists get to evaluate their views according to their own internal standards when Catholics do not. (I'm guessing Catholicism will turn out to be well-justified when judged on its own internal standards.) Buddhism is not called harmlessly silly; it is called a beautiful and noble tradition that Flanagan personally thinks is irrational but which might qualify as rational (apparently) under its own standards.
I have no particular dislike of Buddhism; I suppose it might have a moral majesty beyond anything the Catholic Church has created, and the possibility of harm from this system of belief may be much more remote than the possibility (or actuality) of harm caused by the Catholic Church. But I do not see how this justifies treating Buddhism as having its own epistemic standards and moral majesty whereas Catholicism is "silly" and possibly "dangerous" when it does apparently the same thing. For whatever reason, Flanagan inconsistently gives far more credit to Buddhism than he gives to Catholicism for the same epistemic sins.