I personally hold the view that these labels (monotheism, polytheism etc) are foreign to the very nature of various faiths. Take Islam for example, it is commonly classified as an Abrahamic monotheist religion. But it a-priory adopts the position that in all nations and all lands God's message has been propogated by messengers and that its message is not something new but another call to the same message. (for example see the Quranic verse 4:163). This renders the idea of it being "Abrahamic" pretty much meaningless for then "Abrahamic" can be replaced by any other messenger's name. The word Abrahamic conveys a limited and exoteric understanding of Islam.
The concept of monotheism, meaning one God, is also a limited way to understand Islam. That God is one, assumes the position that the terms God and one are firstly understood. But God/Ultimate reality cannot be completely understood in any fixed way as per the Quran, and there are even monist verses in the Quran which indicate that his conceptualization as a distinct deity may not be complete understanding of Him. Similarly for one-ness the word Islamic understanding of Tawheed is much broader, and Unity (wahdat) of God has a scope which leads to panentheistic concepts such as Unity of Existence (wahdat ul-wujood). In Islam God is one, but not in the sense of counting, rather in the sense of there being no similar likeliness of the Ultimate Reality and there being no multiplicity concerning that Reality.
Hazrat Ali stated,
To know God is to know his oneness. To say that God is one has four meanings: two of them are false and two are correct. As for the two meaning that are false, one is that a person should say "God is one" and be thinking of number and counting. This is false because that which has no second cannot enter into the category of number. Do you not see that those who say that God is a third of a trinity fall into this infidelity? Another meaning is to say, "So-and-So is one of his people," namely, a species of this genus or a member of this species. This meaning is also false when applied to God, because it implies likening something to God, whereas God is above all likeness. As to the two meaning that are correct when applied to God, one is that it should be said that "God is one" in the sense that there is no likeness to him among things. Another is to say that "God is one" in the sense that there is no multiplicity or division conceivable in Him, neither outwardly, nor in the mind, nor in the imagination. God alone possesses such a unity.
I think people have caused this division driven by a need of a scientific classification of faiths without understanding their esoteric and real character. A book which addresses this is Schuon's Transcendent Unity of Religions, where it is essentially argued that the reason why in many cases people searching for unity between these seemingly diverse positions of x-theism (x=mono, poly, dualism etc) is that they are searching for unity at a theological or exoteric level where it doesn't exist. To find real unity is to gain knowledge of an esoteric level where these distinctions start appearing as different perceptions and the Truth appears stripped of them.
Once you adopt the above position the question as stated would itself lose its basis.