See also the linked Topic
Critical Theory
The main approach is similar to Marx’s idea of oppressor/oppressed groups, 'classes'. Marx limited that mostly to economic resources, either having them or having access to them - the 'means of production'. Although a number of nations tried this redistributing of wealth none have been successful, rather a 'redistribution of poverty'.
This is partly due to the doctrinaire approach that treated dissenters (who often had better practical skills) as traitors and thereby removing perceived opposition, but actually, they were the people you needed to prosper, and who were willing to help.
It was also due to the implicit political power structure where, despite calling themselves 'democratic', ordinary citizens were not allowed genuine choice, as the leaders of the 'permanent revolution' knew better and would let you know what you needed to do and what your opinions should be (the party line). This resulted in the exact opposite of what was advertised.
No political system is perfect but some are less perfect than others. Churchill said:
'democracy is the worst form of Government except for all those other forms that have been tried from time to time.…'.
This system generally requires a meritocracy - the best people are given more responsibility. However there are those who want personal power of various sorts (position, money, reputation) but don't want to cooperate with the existing system. They seek a different path. They may personally resent and hate those who are prospering in different ways.
Critical Theory then provides this path. The reason you are not doing so well is because others are oppressing you. This is not focused on money - at least not in a socio-economic class sense, because upward mobility is actually quite accessible. Instead the attributes had to be harder to escape - like gender, or skin colour, or sexual orientation. The more 'intersections' of these you had the more oppressed you were, and the more reason you had to demand redress.
This worked best when there were issues like the gender pay gap, racism, or opposition to same-sex relationships. But the answer was not just to address these issues (which largely happened) but to declare the oppressors morally flawed and degenerate and only worthy of reduction to a subservient status. It's not reform, it's replacing one system with another that is more partisan, unfair, and economically disastrous for most.
Racism
The most successful recent campaign for the Theories is Race - not racism as such, but Anti-whiteism (which of course is racism). The tactic of blanket accusation "you're all racist" by BLM was common. We know of the one who is 'the accuser'. BLM were the successors of the Black Power Movement that Martin Luther King spoke out against.
But why did so many institutions (not least the Church of England) in the West acquiesce to this while people like Trevor Phillips ex-chair of the Equalities Commission said that the UK was not 'institutionally racist'.
What of the fruit? BLM leaders have become rich, and neighbourhoods that need help did not get it - crime rose due to attacks on police funding.
Christianly
"The root problem with CRT isn’t sociological—it’s theological. It makes claims about humans, guilt, and redemption that are fundamentally at odds with what God says about us in the Bible." William Wolfe
Western elites adopt ‘woke’ Post-modern ‘Theory’ as it has an ideology that allows you to make up facts – so you can assert that whoever your opponents are (your 'oppressors') (even the general public) - they are irredeemably wrong and so can be overruled. Any facts marshalled against you can be dismissed as being used to oppress you and are therefore not valid. The old Enlightenment idea (derived from a rational God-ordained view of the universe) that reason and evidence are key is no longer held to be true by woke elites.
“Within the philosophical system of Marx and Lenin, and at the heart of their psychology, hatred of God is the principal driving force, more fundamental than all their political and economic pretensions.” Aleksandr Solzhenitsyn @AI_Solzhenitsyn
Larry Taunton compared the influence of Christian and atheistic teaching in Karl Marx vs Charles Spurgeon - An Epic Struggle for the Souls of Men in 19th-Century London. Spurgeon spoke about the darkness in our hearts and the light, freedom and joy Jesus brings. He had congregations of thousands. Marx spoke of the darkness in the system and how it could only be expunged by bloody revolution. Britain did not warm to this and instead his creed infected millions overseas with deadly effect.
Here he gives a quick review of how many of these ideas are playing out today in the West.
But what are they really after?
"I'm often asked, 'What is the endgame of Critical Race Theory?' My response: power - and everything that comes with it - wealth, control, and, pre-eminently, an intersectional, anti-Christian society wherein Marxism serves as its foundation and ethnic partiality as its cornerstone". Darrell B. Harrison
"Leftists used Critical Race Theory to make gender theory and queer theory more acceptable, and many of you fell for it. They don't care about black people, and they don't care about homosexual and transgender people either. They only care about using people to gain more power". Samuel Sey
There are methods
“The whole aim of practical politics is to keep the populace alarmed (and hence clamorous to be led to safety) by an endless series of hobgoblins, most of them imaginary.” H.L. Mencken.
Included in these are exaggerations of Racism, Slavery, Covid (WHO/Government), Climate. All these require suppression of inconvienient facts and vilifying any who contradict them.
Use neologisms - invented words - to seek to create new meaning when it is often a smokescreen to sound profound when there is nothing there, a hollow shell.
Saul Alinsky was instrumental in his book 'Rules for Radicals' for providing a methodology for dismantling the current system to take power. An outcome of this was systematic election fraud in the US through the ACORN organisation - ironically funded by the US Government. David Horowitz, reformed leftist radical unpacks this: https://www.youtube.com/watch?v=gRUP5yEm1WE. He also explains Barak Obama's role in ACORN in Barack Obama's Rules For Revolution: The Alinsky Model.
“The issue is never the issue. The issue is always the revolution.”
Woke warriors will often strongly imply the law is on their side (and maybe they choose to believe it). Once we have the courage and resources to challenge them we typically find it does not (eg Non crime hate speech, Gender criticism)