So, in terms of intellectual thought, there was a strain of thought referred to as the Frankfurt School that discussed a thing they called 'cultural Marxism'. Some of that discussion was about what we'd now think of as PR/propaganda - promoting socialist/Marxist thought.

In terms of right wing PR/propaganda, it is another example of them following a specific playbook to redefine a term to mean what they want it to mean. 'Critical Race Theory' is the current example of this; 'political correctness' was another. Remember when they were shouting about Saul Alinsky? Well, that was because the playbook is largely derived from his writings - specifically, the tactic described as 'Pick the target, freeze it, personalize it, and polarize it.'

So there you are. Depending on your politics, it was a strain of Marxist intellectual thought in the 1930s, or just another cudgel in the culture wars.

Critical theory is actually what people mean when they say cultural Marxism.

Critical theory itself came out of various Marxist and Marxist-influenced academics in the mid-20th century.

Marx wrote about a theory of history in which all of history progresses through phases in which each phase is defined by struggle between classes. His view was that communism was the inevitable end of this model of history in that communism would finally resolve the class struggle. But for somebody who wishes to promote communism, the problem is if there is no class struggle, then history does not advance to their desired end state.

The original formulation of Marxism was economic, based on the struggle between the proletariat and the bourgeoisie. This conflict worked to create communist revolutions in nations with more feudalistic systems like Tzarist Russia. However Communists have struggled to create revolution in more Democratic societies with greater social mobility, or at least the perceived possibility of.

So failing to get the economic class consciousness to trigger a revolution, the modern Marxist has moved on to pushing race/culture based class consciousness as the trigger for their revolution. This is why todays Marxist is not obsessed with rich and poor but white vs black vs hispanic.

A worldview which sees only The Oppressed and The Oppressors, and maps people into one category or the other. For Marx class was used, now it's race... and complete bullshit.

Cultural Marxism is a revolutionary leftist idea that traditional culture is the source of oppression in the modern world. Cultural Marxism is often linked to an insistence upon political correctness, multiculturalism, and perpetual attacks on the foundations of culture: the nuclear family, marriage, patriotism, traditional morality, law and order, etc. Cultural Marxists are assumed to be committed to establishing economic Marxism, in which case their cultural attacks are a necessary preparation for their ultimate goal.