A few thoughts, FWIW.
I don't think that looking to modern expressions of polytheism (e.g. Hellenism, Asatru, Romuva) is particularly useful in trying to illuminate the - rather odd - D&D religious worldview. Nor do I think that looking at certain aspects of contemporary Hinduism has much to offer: as much as a continuity with antiquity is more demonstrable, modern Hindu polytheism is still very much a product of modernity. Contemporary religions are a function of contemporary times, with regard to their mores, praxis and worldview.
The default D&D paradigm seems to be - largely - one of monolatry. I have my patron god, you have yours, and while we each accept the existence of other deities, we each - for whatever reason - believe that ours is the "correct" deity to worship. This brings D&D religion most closely into alignment with Bronze Age or Iron Age patterns, where different cities or ethnopolities had a tutelary deity - except, in the case of D&D, this worship doesn't seem to be particularly localized (although more so in Greyhawk than FR). Which is to say, it doesn't really resemble anything in our own world's history.
I don't find nontheism in a D&D setting particularly implausible. Unless someone - along with a group of other people - witnesses the manifestation of a deity in their full majesty, I think that denial is entirely reasonable.
A deity appeared to me [it was an episode of madness]
We encountered an angelic servant of a deity [it was not what it claimed]
The priests of Heironeous use divine magic [its source is not what they claim]
Etc. etc. And given how humans are adept at denying demonstrable, replicable facts (think flat-earthers and vaccine-deniers) in order to accord with their existing worldview....
People may otherwise view deities as merely entities of a different order, impostors, useful allies, symbolic constructs, objects unrelated to the pursuit of spiritual truth, phantoms or hallucinations, irrelevant, or simply nonexistent. Regardless of their specific position, they don't deem deities worthy of worship.