To be fair, the main critique of Christianity by Jews was (and still is) that it violates the first commandment, and the handwaving about the nature of the Trinity is just a cover for polytheism. I don't think a syncretic Christianity that feels very polytheistic is implausible at all; the issue is syncretism with the Roman religion, when Jesus's whole narrative about being the Messiah came from a distinctly anti-Roman Jewish tradition.
Well, that's the Islamic critique of Christianity too, with the strongest objection being to the idea, horrifying as I gather they conceive the nature of God, of the Incarnation.
As someone who long ago dropped out of any kind of Trinitarian piety and more lately actually has a hard time taking the concept of a God like the entire Abrahamic complex takes God to be--Creator, all powerful, all knowing,
and loving--but was once pretty seriously engaged in trying to take orthodox trinitarian Christianity seriously, I don't find the concept of the Trinity at all problematic--if only we stipulate this God person exists at all. Given that, the Incarnation is a pretty wonderful, if also appalling from some points of view, concept, and in no way opens the door to a generic polytheism or pantheism. Surely it might be possible that say Krishna or some mythic figure of various Native American peoples might possibly also be incarnations of the Almighty, and one could argue that if God can take on the aspect of a human person in one context, God can also be a different human person in another context...speculatively. But given the integral nature of the Almighty as omniscient and entirely competent, and not a Trickster but the very fountainhead of ethics and morals, which of course disapprove for good reasons of deception of any kind, it seems more sensible, when I take the "angels' advocate" position of theorizing about a stipulated Abrahamic God, that any incarnations of God would be the same human person every time--though it would hardly phase me to have this incarnation of the same Person being sometimes male, sometimes female, and of course of any ethnicity one could name. It is of course trinitarian orthodoxy that it is superfluous for God to incarnate more than once, but I think that is an unnecessary dogmatic restriction of free thought; we can't presume to know whether it might seem fit to God Almighty to incarnate just once versus trillions of times in the Cosmos and even dozens just here on Earth.
But insofar as Jews or Muslims believe that the Trinity itself is polytheistic in nature, I respectfully submit that while that might be true of some particular conceptions of it some people might have, it is not an accurate understanding of what it must be for everyone. The concept of One God manifesting in several aspects to human perceptions, given our mortal limitations, is not inherently polytheistic, and one would have to expand the idea of "a syncretic Christianity that feels polytheistic" concretely to discuss whether it really fits as Christian at all.
My working definition of Christian is that in some sense or other, the professed Christian accepts Jesus Christ of Nazareth as "the way, the truth and the light." It does not have to be exclusive of people who do that in a very different spirt that what I understand orthodoxy, as championed and influenced by the Roman imperial regime (that is, Eastern Orthodox, Roman Catholicism and most Protestant reforms of the latter) frames and stresses, despite the apparent misunderstandings of Mohammed or if I take you at your word, Talmudic perspectives, in common with these monotheisms the strictly unitary nature of God. As I understood it being raised Catholic and reading a lot of CS Lewis on the side, it is not weird to believe that the Creator, Jesus, and the Holy Spirit are all one thing that appears to humans in very distinct aspects but still is one integral solid whole, which we just don't see as that so easily. But all the teachings I ever had stressed that we bear that in mind as a true statement if indeed a Mystery--the Mystery of the Trinity. One can dismiss that as a cheap authoritarian imposition and a rhetorical misdirection trying to mask a flat contradiction, and many an apologist has leaned on that kind of persuasion to shut up questioning, but I believe if one understands what a Mystery is--not just as we colloquially say, a puzzle we have not solved yet, nor necessarily a lie, but rather that there are aspects of our reality that just don't go well into words and logic and need to be approached in a different frame of mind--then it is not unreasonable to uphold the Mystery of the Trinity, and claim to be both a follower of Christ and a strit monotheist.
So if you have no problem with a Christian denomination that is clearly and reasonably Christian, and yet also plainly polytheist at least in feel, please outline what that would look like to you. Surely in 2000 years, quite a few individual professing Christians and some regional state backed or highly popular insurgent sects have in fact provided some examples I suppose, but it seems quite mistaken to me to suggest that the big well known orthodoxies, Catholic of either division, Protestant, or even as far I dimly understand them the various other orthodoxies--Nestorian, Monophysite, or whatever--actually went in that direction. Would you give the Latter Day Saints as an example? I also understand them only dimly--I mainly have a sort of political stance, balancing on one hand a perception they tend to line up with some notions I find pretty reactionary and authoritarian versus the knowledge that they have suffered persecution, misunderstanding and misrepresentation to come to a kind of secular push position, per American religious freedom notions--if they aren't "Christian" at all, they darn well have a right to that, but as I understand it, they do continue to hold Jesus in a supreme position, if perhaps subordinate to God Himself--but that is no different fundamentally from Arianism, which I think is plainly also Christian. As understand it they have a sort of continuous creation model, in which the lord of a particular world creates mortal beings who, if they live righteously, can hope to someday themselves become lords of another new world they create in their afterlife. Whether they revere Jesus as an aspect of the one true God lord over this fractally multiplying and open-ended eternal multiverse, or rather just as "the Savior of this particular Earth," would be the criterion for whether they are in fact a kind of Christian polytheist--for the latter view implies that off in some other dimensions, entirely different Gods are manifesting as a completely different Savior, or perhaps don't take that tack in their particular bailiwick at all, and if there is some integrated ultimate Lord of all, it might in that hypothetical case have an entirely different aspect than the various Christian orthodoxies, including say Arianism, all agree on. If the One True God is quite different than Jesus, rather than Jesus being a true face of that one God, then we might have polytheistic Christianity...though that would look and feel a lot different than Hellenistic Olympian pantheons being integrated into something else that is indeed recognizably Christian!
I was a little tongue in cheek but also serious giving my own example, Tolkien's subordination of the generic form of an Olympian (or Nordic) pantheon into a Christian orthodox frame, which logically allows them only to be faithful, or in some cases unfaithful, angel figures. But the character of obedient agents of the will of one true God is quite different than the quarrelsome, morally dubious figures of Hellenic Olympianism, and the moral makeover into something morally acceptable to such a straightlaced Catholic scholar as JRRT quite transforms the general character of the mythos. Anyway this feat of his creative imagination, basically peculiar to him (though I have to wonder how many Christians nowadays have seriously incorporated the idea that the Maiar as he describes them in the Silmarillion and other works as literally true of God's actual angelic agents; Christians of a Valar rite then) was only possible because folk religion taking old pantheons seriously was pretty well exterminated and had a long cultural distance placed between himself and its living practice--I have long ago explained here why I think any attempt to work the Olympians into Roman Christian orthodoxy would have been quite disallowed; much too dangerous and subversive of the core message. It is not unreasonable to suppose the One True God of Abrahamic tradition would create a cosmic bureaucracy of supernatural powered beings dedicated to particular aspects of the cosmos, but the pragmatic politics would have been far too risky when the faith was trying to take root. Of course syncretism means that vice versa a certain tolerance of folk notions of equivalence between their traditional peasant pantheons and aspects of the "true" monotheistic religion more or less lubricated the ascendency of the latter and infused themselves into the evolving orthodoxy, but I have also described the difference between such grassroots permeations and a top-down state approved orthodoxy taking that claim and running with it from the get-go. We can say Christianity is a Hebrew base syncretized with Hellenistic
philosophy, indeed, but that philosophy had to be purified of its pagan antecedents and held to be the true reasoning of virtuous pagans discerning a truth beyond the veil of their illusions, and indeed I believe the pre-Christian Hellenic philosophers were themselves trying to get away from traditional pantheism toward an alternative and in their minds superior truth; what the Christian "fathers of the Church" did was hand this to them in a neatly wrapped up and mythically satisfying package.
So the challenge here is to have
more syncretism with Hellenistic non-Hebrew prevailing traditions, when I think that actually it took in the maximum amount that it could possibly do--technically we can go anywhere with this rather, but in terms of producing a functional package that went viral and took over the civilization and put down deep and spreading roots, the syncretism we've got is optimum. To try to mix it with more paganism, get more distant from the Hebrew Abrahamic roots, would I think kill it as a strong competitor for orthodox establishment, and what the Emperors needed was that. In fact I am confident that all sorts of hybrids were developed, held as personal views of this or that person and preached and promoted, and this process continues, and this stuff has a certain niche, but if it were viable as an ATL orthodoxy, why that is what would in fact have evolved!
From Jewish roots, synthesizing with Hellenism, we get the churches we've got in other words. They do span a wide spectrum but I don't think the perception Jews and Muslims may sincerely and reasonably have of all these Nazarenes being one big mess of crypto-polytheists do justice to the true subjective viewpoint of most of them.
And as someone who obviously enjoys speculations on these lines, I would love it if you proved me wrong with a vigorous counterexample, one that either you point to from real history or current practice, or one you dream up all by yourself!
Of course I realize that for believing people, this is playing with fire. If the God of my upbringing, the Trinity as presented by Roman Catholicism, were exactly as advertised, I am going to hell for apostasy, blasphemy, and fooling around with counterfactual mythologies to be purportedly taken seriously by some ATL people is a great compounding of these sins--indeed a clever person might lead an otherwise OK person into the gates of Hell by misleading them with a sufficiently sound alternate theology!
But that is the risk anyone on this thread runs of course. To the believer, any sort of confused insanity is possible, more or less depending on plausibility, but there is one truth, and from such a point of view, it could not have been otherwise than in reality because one of the faiths people hold to in real life OTL is in fact the true one, and that could not be otherwise. How much in mortal peril others are in depends on their personal relationship with the true God I suppose, that's how I understood the Catholic message in post-Vatican II days (that council was going on when I was born, so my whole Catholic consciousness is post VII). A person raised in the wrong religion might be saved because their errors are not their fault, perhaps, depending on whether their lives took them closer to the truth, whether they opened their hearts to true wisdom, and in their fallible ways accepted, perhaps without knowing it by the right names, the grace of the true God.
But for me to set up a pulpit and say "let's pretend Aphrodite was actually some kind of angel!" is definitely culpable!