One of the more serious criticisms that Islam and Judiasm have directed towards Trinitarian Christianity is that such a belief system is inherently polytheistic. Indeed, part of the reason why certain strains of Islam persecute Christian minorities is because polytheism is such a serious offense under Islam (and that norm derives from the Old Testament).
Unitarian Christianity also rejects the Trinity as polytheistic. Given that unitarians have tended to be more socially liberal since their inception, I don't think they desired to persecute Trinitarians or assert that belief in three gods is a serious "moral crime," but rather argued that believing three gods are really one God is illogical and hence error. The (small u) unitarians of the founding era (which arguably includes the most influential framers -- Washington, Adams, Jefferson, Madison, Franklin & others) tended to be Enlightenment influenced and believed in viewing traditional Christian doctrines through the lens of "reason." And if there was one thing that was "unreasonable," it was that doctrine.
For instance, here is Jefferson describing that doctrine (read the whole letter; his critique of the Trinity is devastating): "The hocus-pocus phantasm of a God like another Cerberus, with one body and three heads, had its birth and growth in the blood of thousands and thousands of martyrs."
Here is Adams (who was a capital U Unitarian) in a letter to Jefferson: "Had you and I been forty days with Moses on Mount Sinai, and admitted to behold the divine glory, and there been told that one was three and three one, we might not have had the courage to deny it, but we could not have believed it."
But let us assume that the Trinity is compatible with monotheism: three different variations of the one God. If it is, then there are other historic religions, commonly regarded as polytheistic, that could just as logically reconcile themselves with monotheism as does Trinitarian Christianity.
In America, reconciling with monotheism is important because the Declaration of Independence alludes to a monotheistic "God of Nature," who by the way, is not identified as the God of Scripture, even if in the minds of many in the population (but not the Declaration's drafters or doctrinal formulators) He was.
Hinduism is a classic example of a religion that is as reconcilable with monotheism as is Trinitarianism. But instead of only three different versions of one God, there are many many more. From what I have read, this is indeed how Hindus understand their faith.
From this article:
The Vedas tell us this about God - "OM Poornamadah Poornamidam Poornaad Poornamudachyate; Poornasya Poornamaadaaya Poornamevaavashisyate". Translated in English, this verse means "What is Whole - This is Whole - What has come out of the Whole is also Whole; When the Whole is taken out of the Whole, the Whole still remains Whole". The essence of this verse is that the Infinite cannot be measured arithmetically - God is Infinite. The Infinite can be represented in Infinite ways and does manifest in infinite ways. This, in short, is the essence of the Hindu belief in God. That He is everywhere, aorund us and within us. Infact, Hinduism takes the bold step of proclaiming that "we are God".
At the end of the day, Hinduism is monotheistic (Believes in One God). However, Hinduism believes not only in One God, but also in His Infinite manifestations around us and within us perpetually. Realizing that it is impossible for mankind to visualize the Infinite, Hinduism presents us with His forms to help us visualize him. This belief of Hinduism is often confused with polytheism.
To illustrate this point - We all observe the unending processes of birth, existence and death, which seem to be continually taking place around us. We constantly witness these processes and are yet ignorant of them, living as we do in the comfort of our illusory lives. Hinduism gives form and shape to these "works" of the Infinite with the Hindu Trinity - Brahma, Vishnu, and Shiva. "Brahma" creates, "Vishnu" sustains, and "Shiva" destroys or consumates everything in the Universe.
That the Supreme can be worshipped in any form is a concept unique to Hinduism. Such worship is truly a tribute to His greatness.
It seems to me that no intellectually honest Trinitarian Christian could ideologically bar Hinduism from the realm of monotheism, if Hindus do indeed wish to be understood as "monotheistic."
In any event, we should want to include Hinduism into the ranks of monotheism to "cover our bets." For all we know, this is the indentity of "Nature's God," as opposed to this.