Polytheism is the belief in, and often worship of, multiple deities or spirits, which are usually assembled into a pantheon of gods and goddesses, along with their own religious sects and rituals. Polytheism is a type of theism. Within theism, it contrasts with monotheism, the belief in a singular God who is, in most cases, transcendent. In religions that accept polytheism, the different gods and goddesses may be representations of forces of nature or ancestral principles; they can be viewed either as autonomous or as aspects or emanations of a creator deity or transcendental absolute principle (monistic theologies), which manifests immanently in nature (panentheistic and pantheistic theologies). Polytheists do not always worship all the gods equally; they can be in monolatrists or kathenotheists, specializing in the worship of one particular deity only or at certain times (respectively). The recognition of the existence of multiple gods and goddesses, however, does not necessarily equate to the worship of all the deities of one or more pantheons, as the believer can either worship them as a whole, or concentrate only on a specific group of deities, determined by various conditions such as the believer's occupation, tastes, personal experience, family tradition, etc. It is also possible to worship a single deity, considered supreme, without ruling out the existence of other gods. This religious position has been called henotheism, but some prefer to call it monolatry. Although the term "henotheism" is controversial, it is recognized by scholars that the worship of a single God accompanied by belief in other deities maintains the principle of polytheism. - Wikipedia
In the following article, quoted in part, the claim that the LDS Church is polytheistic is denied:
Latter-day Saints are not polytheists in any reasonable sense of the term that does not also exclude most other Christians who deny the Modalist heresy - fairlatterdaysaints.org
A distinction was attempted by Apostle Orson Pratt that, although there have been, are, and will be an unknown number of Gods as the process of begetting and deification continues there is only one God (principle of truth, light, and knowledge) and this God, often personified but who is no actual being, inhabits or may inhabit an unknown number of "temples" which are also referred to as Gods. The God of the Bible, the Heavenly Father, then, is one of these "temples" as is the Son now and someday so shall all who achieve or inherit Christ-likeness. Additionally, Heavenly Father once was a man such as Jesus was and became God the being (the temple housing God the principle) at some past point just as Jesus did.
This opinion was opposed and ultimately excluded from official LDS teaching, primarily on the grounds that Pratt's conception of God/(s) having reached a condition of complete knowledge (omniscience proper) conflicted with then President Young's insistence that God/(s) knowledge eternally increases. Neither ever wavered from the doctrine that an unknowable number of Gods exist. The definitions appear widely variant however with Pratt's Gods having arrived at perfect knowledge and Young's Gods forever perfecting knowledge.
One of the denials of polytheism appears to hinge upon acknowledging the existence of multiple Gods while at the same time only worshiping one of them. This seems to fall within the category of henotheism which, according to the Wikipedia article quoted above, does not fall outside the lines of polytheism.
Monotheism claims that there is only one God anywhere (multiple universes or not); it speaks of ontological being rather than unity between beings. It allows for the existence of other beings who may claim to be God but does not allow for them to be true.
The LDS claim to monotheism seems to appeal to the oneness of the various Gods while maintaining the insistence that Father, Son, and Holy Spirit are distinct beings. Of the unknowable number of Gods which exist (unknowable because they are outside of our universe and no revelation of them is given) there are at least 3 distinct beings who are each God. To Latter-day Saints, the Father, Son, and Holy Ghost are 3 distinct beings, and these members of the Godhead have perfect unity in purpose and plan. Our worship goes in one and only one direction.
What do LDS adherents worship, the unity between the Gods or the distinct God's themselves? If it is 1 of 3 distinct God's who are but some of many, how then are they not polytheist? If it is the unity between the Gods, how then are they not pantheists (Pantheist belief does not recognize a distinct personal god, anthropomorphic or otherwise, but instead characterizes a broad range of doctrines differing in forms of relationships between reality and divinity.)?
Note - A significant edit has been made to this question on the basis of comments and further research. I have endeavored to remove a quotation that appeared to be official LDS teaching but was not without obliterating the heart of the question itself. Apologies if some answers are invalidated by this action.
