"... "polytheism" doesn't require hyphenation in the case of multiple deities. It is only in the case of a belief that deities are not independent beings that such clarification is necessary. From an anthropological standpoint, polytheistic societies acknowledge multiple independent godlike Powers, regardless of the underlying cosmology. Plenty of traditional polytheistic societies have a concept of "oneness" (and plenty don't), but in those cases, the "Oneness" is rarely the focus of veneration- it's simply a cosmological idea, not a theological practice.
Perhaps one of the reasons that the "devotional" or "hard" polytheists are so adamantly defending "polytheist" as meaning only traditions in which the gods are real and distinct is because, from a historical perspective, that is true. I can't think of a traditional religion in which shamans or priests to say "I ask Spirit"- no, they generally ask "the spirits", "the ancestors", or "the gods". Any tradition that reduces the cosmos (or even just divinity) to a single entity is supposed to have "mono" in the title somewhere. Describing Athena, Frigga, and Amaterasu as archetypes or undifferentiated faces of a single Power is a belief in "one", not a belief in "many".
To describe such a "mono" religion as "poly" is the linguistic equivalent of calling one person drinking a martini a "cocktail party". One might as well call a rainstorm by the name "water". It is philosophically possible to defend such a position, but it not particularly useful in most circumstances. Why then do so many people so strongly object to a small group of people (Do we call them "Person" now?) insisting on a more precise, historically-accurate use of a term ("polytheism") that until recently had a fairly precise meaning: belief in many gods?
Can't we just cook up new terms for the hyphenated stuff? Polyarchetypicalist? Polyfaçadal Monist? Eclectic Jungian? I mean, monism gets to have a separate term from monotheism- why not let the people who believe in multiple, literal GODS keep the term they always had? Let's just find a new term for people who address Unity through multiple faces."
(the original may be viewed here.)
THIS. precisely this. I would have no argument whatsoever with 'polyarchetypicalist' or "polyfacadal monist." They're much more accurate for one thing, and they do not infringe upon our religious identity.