Suppose that I assign a non-zero probability to some religion, and this religion tells me that a certain action decreases the probability of an infinitely valuable outcome (e.g., eternity in heaven, or avoiding an eternity in hell). If there is no non-zero probability hypothesis on which the action increases the probability of an infinitely valuable outcome (or decreases the probability of an infinitely disvaluable outcome, but I shall count the avoiding of an infinitely disvaluable outcome itself an infinitely valuable outcome for simplicity), it is plain that in prudential rationality I ought to avoid the action.
Suppose that a number of religions have non-zero probability. Then if A is any action such that at least one of the religions claims that A increases the probability of an infinitely valuable outcome (IVO), and none of the religions claim that A decreases this probability, and, further, there are no non-religious hypotheses of non-zero probability that would make A decrease the probability of an IVO, again I ought to refrain from doing A. Now, sometimes there will be a genuine conflict between religions, where one religion tells me that some action increases the likelihood of an IVO and another tells me that it decreases it. In that case, I need to get my hands dirty with probabilistic calculations. I need to compare the IVOs (not all IVOs are equal; eternity in heaven with daily apple pie is not quite as good as eternity in heaven with daily apple pie à la mode); I need to compare the degree to which according to the respective religions A contributes to the likelihood of the respective IVOs, and finally I need to compare the probabilities I assign to the respective religions. These computations involve comparisons of infinities, but that's not at all a big deal—I just use an appropriate non-standard arithmetical model of infinite values.
Except in the rare cases where things balance out precisely, say when there are only two religions of non-zero probability, and they have equal probability, and one says that A increases the chance of an IVO by 0.2 and other says that it decreases it by 0.2, and the IVO is the same, or in the somewhat less rare, but still rare, cases where no religion of non-zero probability says anything relevant about A, these religious considerations will trump all other self-interested considerations. After all, only religious claims involve IVOs, and any change in the likelihood of an IVO trumps any change in the likelihood of something of finite value.[note 1]
Unless the number of religions that I assign non-zero probability to is very small (say, 0, 1 or 2), or there is a lot of similarity between the religions I assign non-zero probability to, taking these considerations into account will lead to a rather unappealing way of life, since there will be a lot of restrictions on one's actions, as, typically, any action that at least one of the religions forbids will be forbidden to one, as it will be relatively rare that an action forbidden by one religion will be positively required by another.
I think this is a reductio of rational decision theory, whether of a self-interested variety or of a utilitarian stripe. (After all, in utilitarian expected value calculations, I will need to take into account any IVOs for me or for others that have non-zero probability.)