This is a broad and intricate topic, so I'll be writing about it in more digestible pieces. I'm also just making these connections, based on some recent readings, so these ideas are all still inchoate, and I can't write down the entire thing all in one go.
Here's the basic outline, though.
America is not just an expansionist state but a transnational empire, so we look to earlier empires for clues about how things will go after ours enters its first major crisis or disintegrative stage.
The most well known example for general audiences is the Roman Empire. For the historical summary, I'm drawing on The Triumph of Christianity by Bart Ehrman. The structural-functional roles played by religion are my own views, though they're straightforward and must be mainstream enough in the sociology of religion (not being an expert there, I don't know the names of whom to cite).
As the Roman state expanded into a transnational empire during the first two centuries AD, it incorporated the gods of the peoples and nations that it subjugated. That made it easier for the imperial center to administer the periphery -- it's easier to extract whatever you want from it on a material level (tax revenue, food, minerals, babes) if you let them continue with autonomy on the non-material levels (language, religion).
At the same time, the subject peoples must also worship the civic gods of the imperial center, such as the Emperor himself. This does not conflict with worship of local gods -- it's an addition, not a substitution, just to make sure the subjects prove their loyalty to the empire, and not only loyalty to their own local group.
This polytheism did not mean everyone worshiped the same large number of gods -- it was mix-and-match, based on who you were loyal to at various levels of societal complexity. There were gods of the family or household, neighborhood, city or town, region, nation, and ultimately empire. And there were various gods who oversaw good fortune in various domains of life -- harvest, childbearing, war, travel, and so on. If your material subsistence was more dependent on travel, you focused more on the patron gods of travelers than other people did.
While this religious pluralism, headed by the imperial cult, served as a glue that held together the expanding empire for its first two centuries, that reversed during the Crisis of the Third Century. That's when Christianity starts to make major strides among Roman subjects, and it culminates in the 4th C., when the Emperor Constantine converted and later the Emperor Theodosius I made Christianity the official state religion of the empire. At the same time, the 3rd C. saw the only period of intense state persecution of Christianity, unlike the earlier practice of tolerance and pluralism.
Unlike the pluralist approach during the rise of the empire, Christianity, which took off during the empire's decline, was monotheistic and exclusivist -- you could only worship one god, and the other so-called gods did not even really exist. You could not be both a Christian and a devotee of the imperial cult, or of the polytheistic array of sub-imperial gods. That disloyalty made it a direct threat to the imperial powers, leading them to crack down on it, especially during the desperate climate of fragmentation during the 3rd C.
But no empire holds together forever, and the decline of the Roman Empire allowed for the flourishing of Christianity.
This seems to be a general feature: inclusive and pluralist during the rise of a transnational empire, to glue together the subjects of a newly united political-economic power, and then exclusivist and not tolerant during the empire's break-up. It allows for some kind of continuity during the disintegration at the material level -- we will still all be following the same exclusivist religion, despite belonging to now separate and smaller nations. Then sometime after that stage, the unity of the religion begins to fragment itself, and regional camps with their own idiosyncrasies evolve, bringing back a kind of pluralism, albeit not under the umbrella of a single polity as before (e.g., Oriental Orthodox, Eastern Orthodox, Catholic).
There's a parallel from the Ottoman Empire, which was religiously tolerant and pluralist during its rise (the millet system), and then saw the seeds of Islamism begin to grow during the empire's declining stage of the 19th C. Once the empire broke up circa 1920, exclusivist transnational Islamism took off in its former colonies (e.g., the Muslim Brotherhood in Egypt, and by 1980 in Turkey itself), but not in places that the Ottomans failed to conquer (Iran, where a pluralist Shia council is in control, or Saudi Arabia, where the militant Salafi jihadism took root, rather than the peaceful political infiltration model of the Muslim Brotherhood, who are their bitter rivals).
Other examples from Muslim history include the pluralism of Al-Andalus during the rise of the Emirate of Cordoba (the Umayyad dynasty's branch that ruled Iberia), which gave way to intolerant and exclusivist waves during the decline (the non-Umayyad Almohads on the Muslim side, and the Catholic Kings on the Christian side). Then there was the pluralism of the Fatimid Caliphate, whose decline and replacement by foreign mercenaries (the Mamluks) saw the emergence of bitterly exclusivist schools of Islam led by, e.g., Ibn Taymiyyah (from the Hanbali school, and inspiration to today's exclusivists and fundamentalists within Islam). In fact, the founders of the Hanbali school themselves flourished during the declining stage of the Abbasid Caliphate, which during its golden age had been pluralist (to incorporate the newly subjugated Persian bureaucrats and administrators).
With that historical and sociological background, let's look at the current situation.
America has been an expansionist empire since its independence, and it began the unification of the 13 Colonies by upholding religious liberty, where various forms of intolerance of certain sects was permitted before. During our rise, an imperial cult grew up -- sometimes called the American civil religion. We worship our Constitution, flag, and supposedly temporal leaders as though they were partly or fully divine, unlike the other advanced nations.
Crucially, this is a distinct religion -- not Christian. We have never said, "In Jesus we trust," or "One nation under Jesus," our flag and other sacred national symbols do not feature a cross, and none of Jesus' or Paul's messages have been at the forefront of the attempt to "put religion back in society" (at best, it's the Ten Commandments from the Old Testament). When we say "God," we're using a weasel-word generic label, "god," but to refer to the patron god of our nation / empire, who provides for and protects us, his chosen people.
He only influences the lives of other people on Earth to the extent that we Americans bring our political-economic rule to them (whether we go over there or they come over here). By implication, other peoples have their own patron gods, who are not as badass as ours is, if they lose to us -- or who rely on tricks and cheating to block our patron god from helping us win, as we deserve to.
That is not the God-the-Father-of-Jesus from the New Testament -- or else there would be some connection to Jesus -- it is not Jesus Christ, and it is not the Holy Spirit. It's a standard patron god of a nation from any old polytheistic society.
The people we subjugate must worship our civil religion, whatever else they do or don't do in religious affairs. Muslim, Christian, Hindu, who cares? As long as you pay material tribute to the imperial center, and pay your symbolic respects to its patron god and imperial cult, our leaders don't give a damn what religious beliefs and behaviors you have. That's equally true for people we occupy and for immigrants here.
Conversely, if you refuse to submit materially to the empire, or if you blaspheme against its patron god and civil religion, you will get persecution and punishment, to coerce you into subject status.
Aside from our imperial cult, there's a wide variety of religious beliefs and practices that fall under the term "identity politics". Some of it is local patron gods for various ethnic groups under our control, some of it is gods who influence our fortunes in the different domains of life (love, sex, marriage, food, child-rearing, etc.). These come in left-wing and right-wing forms, but the polytheistic strand is strongest on the left.
There is a never-ending competition to add more and more gods to worship -- first it was just the pro-black god, then it was the pro-Hispanic god, perhaps generalized into an anti-racist god. Then it was the feminist god, and the gay god, and the tranny god, the vegan god, the environmental god. This is just like the inclusive, pluralist polytheism of the Roman Empire -- worshiping one does not preclude you from worshiping any combination of the others. In fact, most people do worship several of these divine forces.
They worship them to stay on their good side and receive good luck in their personal lives -- and to smite their enemies in their personal lives. These are like the capricious amoral gods of a pre-monotheist society, who can either act for good or for evil, and it just depends on how fervently you worship them, whether you'll be the recipient of their favor or the target of their destruction.
What is the fate of the American imperial cult and idpol-ytheism?
Our empire has been breaking up since our peak during WWII, after which we lost the Philippines and Cuba in short order (both of which we had won by conquest during the Spanish-American War), and we have lost our ability to control "our own backyard" of Central America (none of the right-wing death squads won during the 1980s, and the economic nationalists took over instead, not to mention our repeated failures right now to topple Maduro further south in Venezuela). Aside from losing what we used to have, we have failed at our endless attempts to gain new spheres of influence, all on mainland Asia (North Korea, Vietnam, Iraq, Afghanistan, Iran, etc.).
As our empire declines and fragments on the political-economic level, the tolerant and pluralist tendency will go up in a puff of smoke. It will be replaced by an intolerant and exclusivist moral order -- one whose practitioners cannot worship any of the other gods that are around currently. That could take the form of a resurgence in Christianity, but that religion has been on the long-term decline since the Industrial Revolution.
Rather, the monotheistic replacement will be "socialism" -- in quotes because, like early Christianity, it encompasses several strains and is not a mature ideology or program for structuring society. But unlike all of the forms of identity politics, it makes an exclusivist demand on its adherents -- notwithstanding the fleeting heresy of "intersectionality," everyone understands that socialism is "class-first" (technically henotheist, worshiping one god above other gods) or "class only" and "economic reductionist" (strict monotheism). Marx and other materialists hold material conditions to be the base, and social-cultural features to be the superstructure that stems therefrom.
Again, there will be some diversity of opinion, as with any new religion, but it's clear to see that socialism is not tolerant of elevating other gods to equal status with its own, if it even holds those other gods to exist in the first place. That is unlike all the other leftist, or rightist, forms of identity politics -- being an antiracist allows you to be a feminist, a pro-gay, and a pro-tranny activist. They all have equal standing. Even when identity politics elevates one over the others (henotheism), it does not deny the existence of the others, let alone try to stamp them out, blaspheme against them, and so on.
Socialism makes everything in the moral ordering of society about material conditions, primarily economics. And now, beyond denying equal status to the other gods, it blasphemes them as false gods altogether -- tools of the ruling class to perpetuate the elite material dominance over the masses. This insight of the socialists became especially clear when presidential candidate Hillary Clinton barked back at the class warriors: What is breaking up the big banks going to do to end racism, sexism, and homophobia?
Identity politics serves as a glue to hold together an overly complex empire, which has already begun to come apart. You can't glue it back together, so going forward fewer and fewer people will see any point in trying to enforce identity politics. Nations and ethnic groups under the empire's rule will fragment, and identitarians will be out of business.
As socialism delivers a superior result for people's everyday lives (likely beginning with universal free healthcare), relative to antiracism, feminism, etc., people will start to ignore those impotent gods and only worship the one true socialist god. The one who alone can deliver the goods.
But that also means that socialism is an existential threat to the imperial cult and to idpol-ytheism. Socialists do not revere the patron god of the American empire, and they deny the power or existence of the identitarian gods. So, just as the establishment severely cracked down on Christians during the Crisis of the Third Century, so will ours crack down on socialists as the seams of the empire really start to come apart. There were occasional persecutions of Christians during the rise of the empire, just as there was an occasional Red Scare here during our rise (circa 1920 big-time, and less so during the McCarthyite 1950s). But they will really ramp up during the next pronounced stage of imperial collapse.
Christians could not persecute pagans during the Roman Empire, and socialists cannot persecute the civil religionists or the identity politics people today. Antiracists, feminists, etc., are mainstream and dominant, though not for a whole lot longer. But for now, it's clear who can get their lives ruined -- those who blaspheme the identity gods, not those who blaspheme the materialist / class / economics god.
After we get through the collapse of the American empire, and its former constituent nations and/or regions of the US gain political-economic autonomy, there will be a flourishing of exclusivist socialism. You didn't need to belong to the Roman Empire to be a Christian, and you don't need to be a subject of the American empire to be a socialist and enjoy its superior benefits. Maybe then the socialists will persecute the identity politics heretics, but that's way off in the distance for now.
And after the initial wave of united socialist zeal, it will eventually fragment into regionally appropriate camps, much like the regional camps of Christianity. "Socialism in one country".
And of course, there will be left-wing and right-wing forms of socialism, depending on which coalition is the dominant or opposition for its phase in the regime cycle. During the proto-socialist Mid-20th C., some nations were left-wing socialist (UK, US) while others were right-wing socialist (the Mediterranean). At a bird's-eye-view, they were the same -- populist economic nationalists, only with the military more in control for the right-wing version, and the finance sector in control of the left-wing version.
Left-wingers will have to accept that de Gaulle's France was not a fascist Nazi nightmare, nor was Christian Democrat Italy, both nations whose left-wing party (the Communists) were in the opposition status. They were (proto-)socialist, just run by conservative military types rather than liberal financier types as in the US and UK.
That is the major project for the short-to-medium term -- reach out to normies and right-wingers to unite around monotheistic socialism. Downplay the American civil religion, at least in its imperial cult form, and banish identity politics as false gods preserving the empire. Christianity, Islam, and other major exclusivist religions were missionary and evangelist, converting most of their members from outside the original group. Socialism will never materialize if it is restricted to left-wingers, even those who reject identity politics. As in the New Deal, it needs support from normies and conservatives (the American South consistently voted for New Deal liberal presidents). Socialist mayors did not preside over entire cities during the Progressive Era by only turning out left-wingers on election day.
The monotheist appeal of socialism allows it to transcend all other ideological barriers, unlike antiracism, feminism, etc. It is the only moral vision to unite enough of a society around it to transform it for the better.