Most inhabitants of D&D settings offer prayers and devotion to one deity while acknowledging the existence of other deities. In fact, Clerics aren't polytheists, for most of them pledge their loyalty to a singular deity; they're monolatrists.
Polytheists offer respect and devotion to multiple deities. Most D&D settings have people who may offer prayers to other deities at times, but worship and devotion to a singular deity, or one's patron deity, is still predominant.
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This seems untrue to me. In standard D&D and related fantasy stories (e.g., Skyrim), everyone acknowledges, and reveres the deities as a whole. Or, at least those that they are favorably disposed towards, depending on their level of religiosity and so on (like real people). Usually, prayers are "targeted" towards the deities most relevant to whatever request or task at hand: you pray to the smith god when smithing, the water and weather ones when sailing and so forth. The classic Greeks -- by which I mean the ones from the myths and not the actual people -- follow this model. They famously sacrificed to Poseidon when wanting to make a sea journey. Another good example, which I think captures the default assumption of D&D settings, George RR Martin's Westeros -- the Seven are revered collectively, and you pray to whatever one is most relevant at the time, e.g., the Father for justice, the Warrior before battle. That leads to some correlation between careers or social roles and the deities you're most attached to.
The curve ball D&D throws in is racial deities. Although then they still seem to follow the same pattern b/c D&D has such an extensive set of pantheons. The dwarves have Moradin, for smithing and all-around godliness (he's sort of like Zeus that way), but they also have Clangeddin for the smashing. Even the drow have a few gods, such as Valehroon (sp?), though Lolth wears the pants. If other worship is outlawed, that would make them the exception rather than the rule. I could see racial deities, largely b/c no one can remember all of them, falling into monolatrism -- the elves all call on Correllon for everything.
As to clerics, you might be right. I'm not sure. Very few ancient Greek priests (from the stories) were priests to a specific god. They tended to be more general, following the polytheistic "who do I need to talk to today?" pattern described above. The Romans had elaborate temples to particular deities, though these were again mostly broken up by function: Jupiter for augury, Venus for lovemaking and relationship advice, etc.
It's up in the air whether a priest of god X would call upon god Y when Y was more appropriate. This doesn't strike me as weird, and that's given the years that I've bounced around various D&D settings, especially if the gods were in the same pantheon. It doesn't hit my ear wrong to have a cleric of Lathandar call upon Tyr to help him smite some undead with his mace.
Although, to what extent do the default settings in D&D really have pantheons nowadays?
Aesthetically speaking, it does seem a bit odd for clerics to be too monolatrist, unless you have few gods so they cover a lot of territory with their portfolios. Given the breadth of spells a D&D cleric is going to cast in the course of a day, they might touch on many portfolios. Having a few gods to call upon, based on intercessions, shared interests, etc., might make that more sensible.
