That's backwards. There's a barrier of credibility that skepticism needs to overcome in this case. It is not uncommon knowledge in the base D&D setting that A.) "magic" is real and B.) divine and arcane casters claim their powers are distinct. The clerics of a slew of competing gods assert that their deities are actually gods and provide repeatable supernatural phenomena. Visit any trade city in on Oerth or the Realms and this is painfully obvious. On the other hand, the counter-claim lacks evidence and most attempts to disprove divinity can or have been systematically debunked. One would require a remarkably heavy emotional ax to grind to embrace the denialist position in such a case.
It's not "trust in intellectual authority," it's trust in repeatable phenomena - historical evidence. Attempts to undermine the credibility of witnesses is a time-honored tradition, but in such a setting you're basically alleging a truly grand and sweeping conspiracy to falsify evidence that transcends all animosity between cultures, religions, races, governments, and time-periods and has somehow wiped out all evidence of any cynic or skeptic who could employ the same known means to provide contrary evidence or prove a logical contradiction.
We can't have it both ways with the ignorance of peasants. If we take the realistic medieval example, the overwhelming population are illiterate peons (not even burghers) and have the same cause to question most physical places and historical figures that were part of their physical reality. They also historically heeded the more learned religious authority of their time and regarded those asserting contrary views as deluded or wicked. But then there's the obvious fantasy element in D&D. Even the lowly villagers and manor serfs, outside of an ultra-low-magic setting, believe in divine and arcane magics. With all evidence in the affirmative and no evidence to the contrary, they have no rational basis for disbelief in what the religious authorities tell them about the existence of gods. The religious authorities can perform actual magic. The only explanation would be charlatanism, and with outside collaboration the only explanation there would be conspiracy or mass delusion on the part of so many others. They are essentially asserting that "everyone else is out to trick me," or "I'm the only sane man," without any basis in evidence. There we've pretty much got paranoid delusion in a nutshell.
If I tell the peasantry, "There are no gods. Pay no attention to the clerics over there casting spells. It's all fakery," without anything to back it up but cynicism then they are, almost uniformly, going to regard me as a lunatic - and rightly so, considering the merit of my argument.
However, if you get to a level far enough removed from peasantry to be worldly (as adventurers almost invariably are/become unless they stay stuck in a "hopeless farmboy" or "ignorant barbarian" trope for the rest of their lives), you could entertain more complicated arguments. The only problem is then you'd also be at a level to be more closely exposed to the means at which such theories can be easily tested and disproven. Heck, by mid-tier adventurers can see for themselves and conduct their own experiments.
Pure disbelief in the disposition of souls and the reality of deities in the Core D&D setting is requires a level of ignorance beneath that of a civilized peasant or some sort of delusion. Setting changes can obviously shift that, but they typically require playing around with what magic can do in the setting with regards to extra-planar travel and communication. Hence my original point: It is far more rational to posit a moral or philosophical stance that the "gods" are real entities that pretend at Divinity - limited / flawed / transient beings that don't deserve the title though they need / crave worship.
