Arguendo, let’s grant that both Christians* and naturalists have conclusions P which follow from something essential those world views, and which are described like this: “Given P, my picture of the world is extremely implausible, or morally hideous. Still, I see that drawing P isn’t logically necessary, and I can come up with reasons for why it might be false to draw that conclusion, though I never would have entertained these reasons if I were not committed to my system. Therefore, I deny that I should draw conclusion P.”
For a Christian, some plausible candidates for things that would give rise to such P conclusions are puzzles about scriptural inerrancy (like the ones that caused Ehrman to abandon the idea), or the perpetuity of hellfire. For Naturalists, some plausible candidates are well-attested miracles, the specter of eliminativism, or the universal evidence for spiritual phenomena and religious experience.
One might suspect epistemic parity here, but there is a crucial inequality: the Christian believes the essence of his religion is revealed to him by a mind higher than his own, whereas naturalism believes there are no minds higher than our own. The Christian has a rationally compelling case for holding to his beliefs all the way up to the point where they prove logically impossible, but it’s hard to see how naturalism could justify doing the same thing. If God demanded that I believe in Russell’s teapot, I would be within my epistemic rights to believe one was there; but if Russell asks me to believe in the same thing, I can’t very well do so just because it’s logically possible for one to be there.** If God asked me to believe something implausible or that violated parsimony, I am justified in doing so, but the parallel problem for naturalism consists in asking us to believe something that conflicts with our best human sense of how things are, even while there are no truths outside of our best human sense of how things are.
Though I’m generally skeptical about the idea of a burden of proof outside of courtrooms or the more or less arbitrary decision of who get to be the house in a debate, we have a principled reason to say that a Christian has to meet a much higher burden of proof for abandoning Christianity than a naturalist has to meet for abandoning naturalism.
*Throughout the post “Christian” is shorthand for anyone who believes in a revealed religion. The epistemic disparity now discussed would not be found between Christians and Muslims.
**Seen from this angle, we have a certain inversion of Sagan’s “extraordinary claims” slogan. If I believe a proposition is told to me by God, it is reasonable for me to demand less evidence for it than even for a much more initially plausible proposition that I believe is told to me only by a man. As Thomas puts it, the appeal to authority is the weakest proof, except when your authority is God, in which case it is the strongest possible proof. Notice I call it a certain inversion since, being revealed by God is extraordinary evidence, which speaks not just to the importance of the thing revealed, but the power of the evidence involved.