You might like this answer about the history of dialectic argument, and the emergence of Historical Materialism: Relation of dialectics, as of Hegel and Marx, toward Enlightenment liberalism
And, on invented history: Do historians have responsibility in how they decide to depict something?
Picking through for what you seem to be asking:
I am thinking about how dialectical culture is, especially when it
comes to social movements, values shifting or changing, etc.
modern cultural dynamics have some sort of background, precedent
factors that led to them
endless contrarianism and revision
So, you can look at economic cycles. Schumpeter Waves are interesting, the idea that international trade has gone through cycles driven by developing maturing and decay of successive critical technologies. Discussed here: What will humanity do IF and when technological progression ends? Something important is how technology compounds, and accelerates. We find evolution doing that too.
Consider how a market trader with a substantially better model of the economic system, will affect the behaviour of the economy. People might copy their trades, mirror their style of trading, and reverse-engineer their models knowing what kind of predictions they could make. And then - the economy would behave differently! There is plenty about sentiment and 'animal spirits' in economics, and how homo economicus is invalid: the idea markets consist of independent rational agents pursuing only self-interest. But more interesting is the idea there is a feedback loop, and it includes how models of the system, used in the system, change the system. Douglas Hofstadter has this idea about strange-loops and tangled hierarchies, that this kind of feedback and self-reference is how self-consciousness emerges. It's interesting for thinking about compounding, as the model changes the system it models but also becomes part of it, a model can interrogate and inform a system about itself.
Joseph Tainter in The Collapse of Complex Civilisations, suggests that resource depletion, population increase, natural disasters, and other bumps-in-the-road will inevitably hit a society, and that if it fails to develop increases in capacity to face those challenges, the society or civilisation will undergo 'rapid simplification' or collapse, the costs of the level of social complexity won't be able to be sustained. Social trust, a sense that justice is being done, and that capable motivated people will have opportunitues to do well, are a kind of resource that may be less visibly important in peacetime. When war or disaster hits, everyone gets to find out whether people will lay down their lives for each other, or will run for the hills. Wilson and Pickett's 'The Spirit Level' is interesting on how inequality erodes social cohesion. Here I make a game-theory case that 'expanding the circle of moral concern' increases social cohesion and scope of cooperation: Studies exploring the rationale of gender equality
Historical Materialism goes beyond Marx and Engels, with Fukiyama using the method to declare that the end if the Cold War was the End of History, because the 'absolute idea' of political systems had arrived, and triumphed in the dialectic, and all future systems would be built on or from it. It is clear he was wrong. And a huge problem with identifying trends, is that it can feel very satisfying in accounting for the past, but is terrible at prediction. Marx declared Historical Materialism a science, and Popper clarified the bounding-definition of science to exclude it (and Freud). The actual science of social change is Sociocultural Evolution.
Erica Chenoweth's research pointed to the idea there is a critical threshold for revolutions to succeed, in her book Why Civil Resistance Works: The Strategic Logic of Nonviolent Conflict, and discussed accessibly eg in this BBC article The '3.5% rule': How a small minority can change the world. In this picture it takes the build-up of a constituency behind a cgange, and a representative or group to enact it. So it would nake sense how a clear critique has to emerge, and a change to fix it, for an iteration in system to occur.
As @Rusi notes, the 'myth of progress' is primarily a political motivation of 'progressive' leftwing politics (although by no means always, like the Nazis), and I'd also look to how Marx was explicitly in pursuit of utopia, and Fukiyama pictured a Liberal-Democracy as utopia. Whereas Fear and Anxiety Drive Conservatives' Political Attitudes, especially opposition to change, social and otherwise. I think a lot can be accounted for about political change, by how building a constituency change tends to cohere around hope or fear. Jonathan Haidt's research suggests whether we feel secure or under threat during our teen years permanently impacts our political disposition towards whether fear or hope most motivates us, and we can link that to the ambiguity-tolerance/intolerance axis in psychology.
In terms of cycles of ideas, Baudrillard saw us as involved in stages of progressive abstraction, towards building hyperalities. Discussed here: How are hyperrealities created psychologically?
when people do not understand that rhetoric is just rhetoric; they do
not fathom a difference between how language can embody a certain
idea, but that that expression may not be that meaningful, since
language is imperfect
Is there a clear line though? What about science rhetoric, that can explain say how to win a war, and have real consequences? Or do you mean failure to recognise something as rhetorical? We have formal and informal fallacies to help us identify bad forms of attempted pursuasion. Philospher Harry Frankfurt identified 'bullshit' as "speech intended to persuade without regard for truth", which we can relate to the Sophists that Socrates despised who only aimed to win arguments, but also to advertising executives, lawyers, politicians, lobbyists, and so on. Socratic Dialogue was core to the founding of Plato's Academy and so of the founding of academia: the good-faith engagement in dispute, towards finding better answers, which will satisfy all participants that they are the best answer.
A sense that your culture has some sort of irrationality or falsehood
or inherent error in it, invites one to refute that false idea, with
some contrary one
That sounds like Sartre's bad faith, our refusal to recognise our actual freedom, about our choices or beliefs. For instance people often make an Appeal To Nature fallacy, to justify why some way of behaving is a certain way, and should stay that way, when in fact we get to choose.
Hume with his Is-Ought distinction got at how while we reason around moral problems, the values we begin our moral thinking from are unreasoned, they are feelings, and that must be the case because how the world is arranged cannot compel us to feel we should behave a certain way.
In Buddhist thought they have the Three Marks of Existence, three inescapable points about how things are, that our intuitions generally mislead us about, and failure to grasp which sets us on a track towards wanting what we can't have, and creating suffering. Of the Marks, 'Anatta', the lack of any unchanging self or essence to things, I think relates to your point about reification. For Buddhists the antidote is to recognise Sunyata, 'dependent origination', or how nothing is truly seperate, nor fixed.
the problem is how hard it is to establish some socio-cultural-moral
theory without it being “politicized”, or partial
Rorty has this term '[final vocabulary]' for this kind of attempt to once-and-for-all settle things. And the problem is, you can satisfy yourself that you have done this, but only another person can say if your answers, your final vocabulary or framing of the way things are, satisfies them.
Can there be any 'pure objectivity?' I put it to you, that objectivity is just reified intersubjectivity, discussed here: What is an objective property?
That is, by sharing experiences, and imagining ourselves in all positions, we think we can not only assemble subjectivities and check them against each other, but transcend them and see a world that does not depend on them. Logically though, we can't. Convergence of evidence, consilience, of what lots of peiple see, is better evidence than what one person saw. It's not proof though as collective hallucinations show.
This isn't just a footnote issue either, for instance if how we experience time is conditioned by what our senses can handle, we could be being deeply mislead about reality, with no yet imagined way to check (and a lack of a quantum gravity theory does indeed suggest we don't understand time though it seems so intuitive). Basic things about how we think reality is, could be only how it is for minds like ours. Indeed, that seems inevitable. Sheldrake proposed that we seriously investigate the nicely radical question [Is the Sun conscious?] Can we reasonably know anything about such a min's reality if it were?