Liberalism and its Anti-liberal Moral Order
I feel I haven't done an adequate job explaining to people that what the Critical Social Justice scholars and activists have been building isn't a new intellectual order, it's a new alternative moral order. The intellectual stuff in all that academic Theory just tries to make that project look serious as something other than what it is. When you intuit that Critical Social Justice is like a new religion, what you're intuiting is that it is a moral order. This is actually explicit in their literature at pretty much all levels going back as far into its historical roots as you might want to go.
The functional moral impulse (or axis, if we follow Moral Foundations Theory) is "liberation from oppression," so it's a liberationist moral order. Put otherwise, it's a religion where salvation has been replaced with liberation from oppression (in this world and not some other). One point of Critical Theory, speaking formally about its beginnings, was to bring moral analysis into the otherwise amoral sciences and "neutral" processes of law. In fact, in today's vernacular, it was to introduced problematizing, as a way to vet ideas morally and reject morally bad ones, from a perspective of achieving liberation, whether they're true or not. It has, in time and seemingly not by the design of the original Critical Theorists (in the famous Frankfurt School), come to allowing the acceptance of false ideas that are believed to advance this moral order or its liberatory agenda. That this will not work is a severe blind spot of the Critical moral order.
The objective from the start of the "Critical" project was to replace liberal democracy with "ideal democracy," wherein oppression didn't limit people's capacities to participate in the full measures of democratic society. This meant evaluating morally on what causes oppression. It also meant defining "oppression" according to its beliefs, which were rooted in sensible analyses, the communist theorizing of Karl Marx, the psychoanalysis of Freud, and myriad other philosophical and proto-psychological and proto-sociological ideas that had much traction at the time. In particular, it was rooted in the belief that the ideologies of society are created by the powerful in society and act in their interests to maintain their power. This notion of power is called hegemony and derives from the Italian communist thinker Antonio Gramsci in his famous Prison Notebooks.
One of the fundamental axioms of the Critical approach is that there are no neutral processes and there are no amoral methods. Therefore, everything must be analyzed according to some (meta)-moral standard, and they chose liberation from oppression. That's its faith.
To bring this into the current moment, say whatever you want about the reasons people do things like get involved in looting (there are many reasons, some of which agree completely with this analysis and have been written down as such). The feeling for many of them and for nearly all the intelligentsia who will rationalize and justify it is that society is oppressive and thus needs dismantling. The thing is, people feel their morals. They intuit them and then rationalize them after the fact (this is a school of thought known as "moral intuitionism," by the way). When someone has been programmed (not just indoctrinated) into a particular moral order, they will feel and react according to its prevailing intuitions, and they will then rationalize them as just and necessary after the fact.
The set of rationalizations for the Critical Social Justice "liberation" moral order is called "Theory." In a faith system, that set of rationalizations gets written down and codified into doctrine or scripture. Theory is that doctrine for Critical Social Justice and the literature rooted in Theory, particularly that published within the academic canon in peer-reviewed academic papers and books published by university presses, is the (rather sprawling) scripture. Theory is a blend of many critical methods at once, even including literary criticism pressed into a tool of alleged worth for social analysis, and it has deep roots in both Critical Theory and postmodern Theory, which it effectively combines for the purposes of doing identity politics. Thus, identity, meaning identity as political identity, becomes the central feature around which liberation and oppression, i.e., salvation, turn in this faith.
We should always strive to be fair, though (and to steal our opponents arguments from them before they can turn them illegitimately back against us). Thus, you can say that any society is the result of an underlying moral order. Sure, fine. This includes liberalism (with liberal ethics). While liberalism has some distinct features that distinguish it from being impugned by such an analysis, if we allow it, the question is what kind of societies different moral and societal orders produce. Theocracies, for example, tend not to be great ones, and we can judge on a lot of standards. A Critical theocracy holds no more promise than religious ones, and given its similarity to the utterly failed communist regimes of the twentieth century, it might hold less.
Contrary to very wide-ranging belief, the Critical moral order is not a liberal moral order. It is, in fact, explicitly anti-liberal. One of the key pillars of Critical Race Theory, one of the contemporary Critical faiths holding much relevant sway today, is fundamental critique of liberalism and a generally anti-liberal stance. Like with its Frankfurt School forebears, Critical Race Theory sees liberalism as a means by which the dominant (white) society fools the subordinated (black and other people of color) into believing they have a fair chance, thus convincing them not to agitate for a social revolution. The "Critical" game is to point at the flaws in advanced liberal societies (which are the least oppressive on Earth) and say, "Well, no one would want to live in liberal societies because look how bad they are. Look how they fail!" This is what critical theory is, ultimately: doing this. Learning to do this. It's completely wrong. Most people do prefer liberal societies where their morals are a matter of personal conscience and result from reflection combined with willful participation in vital communities around them.
Putting liberalism on a level with other moral orders is also a mistake, one so severe that it's virtually a category error (and this claim will really upset the philosophers). Liberal societies are fundamentally different than ones predicated on a particular moral order because they arrange a system of conflict management that can handle pluralism (which is not the same as multiculturalism), which no particular moral order can accomplish (they have to use repression instead). This is no small point. Liberalism is a set of very tolerant approach to managing conflicts that arise between people, ideas, and even moral orders. The first of these is covered by democratic and republican law, the second by science and philosophy, and the third by secularism. It's also no small point that these features of liberalism exist to protect people, ideas, and moral orders from encroachment upon them by other entities. The church is protected from the secular state even more effectively than the secular state is protected from the church.
In particular, liberal societies open themselves up to means of self-reformation. Not just self-reform. Self-reformation. Remaking themselves continuously to better achieve the ideals of liberalism. In the end, this makes room for literally any particular moral order, including anti-liberal ones. In fact, it welcomes this kind of diversity because this diversity enables liberal orders to identify and correct their blind spots, which is the nominal (or perhaps Platonic) goal of Critical Theory (which, like communism, just doesn't work in practice). In liberal systems, you're allowed to be a fundamentalist religious person; you're allowed to be an anti-state libertarian; you're allowed to be an anti-liberal critical theorist; you're allowed to be an anarchist. Liberalism will take it all, tolerate it, protect it and its voice, and because it will do so, it can glean the best from each. This opens it up to the threat of being overwhelmed by anti-liberalism, but it is willing to take this risk for reasons that are ultimately good and beneficial to nearly all (if not all) who live in liberal societies.
This is why liberal societies are different (making analyzing them as though they are not a kind of category error) and better. (Here, I hasten to remind the reader that "better" doesn't have to imply perfect and doesn't even have to imply good; it only has to imply relative superiority.) The reason is simple: if you had to break it down to one observation that shows the superiority of liberal systems, it is that liberal societies tolerate, even welcome and protect, explicitly anti-liberal moral orders within them. They let them exist, let them speak, let them agitate for reforms to the liberal order.
And this is how the liberal order continues to improve itself beyond what any particular moral order can hope to achieve. Tolerance is not a property of other moral orders, not real tolerance, and so it loses out on all of that potentially useful dissent and criticism. Repressive societies are corrupt societies, and they cannot be reformed (except by liberalizing). In Critical Social Justice particularly, "tolerance" explicitly means "repressive tolerance," which is to say the kind of sectarian "tolerance" that exists in theocracies and polices blasphemies. It sells itself as being more tolerant but absolutely isn't. This exists in exact parallel to the "peace" that is implied by universal adherence to just one sect of (necessarily vigorously anti-liberal and fundamenatlist) Islam (necessarily brutally fundamentalist because all others would enable dissent from universal adherence). It's peace through absolute submission and utter destruction of any dissent, individuality, or deviation.
To understand what Critical Social Justice is, you have to understand that it is a moral order first, and a particularly dysfunctional and repressive one, and an intellectual system second (if at all and only by pretense). The intellectual stuff is something between post-hoc rationalizations for these moral urges and jargon-laden window dressing to hide what's inside the Critical cathedral from view. This view clarifies your intuition that it's somehow very "religious" in nature, whether it's a religion properly or not, and it clarifies why you should be treating it as such, both in terms of how you learn about it and how you place its roles in society.