For what it's worth, unlike Christianity, Islam, Freemasonry, etc. there is no such thing as 'cultural marxism'. The modern usage seems to be as a catch-all term used by (literal) fascists and fascist-associated groups for literally any progressive or postmodern viewpoint, but in addition usually has the connotations of 'cultural perversion' and 'conspiracy'. Prior usage seems to be to describe an anti-semitic conspiracy theory (that is in part related to modern usage), and the term as a whole dates back to when it was coined by the German Nazi Party ("Cultural Bolshevism" - Kulturbolschewismus) to describe modernist art movements that they thought were 'degenerative'.
Rational Wiki's second description is incredibly descriptive:
""""Cultural Marxism" (both uppercase) is a common snarl word used to paint anyone with progressive tendencies as a secret Communist. The term alludes to a conspiracy theory in which sinister left-wingers have infiltrated media, academia, and science and are engaged in a decades-long plot to undermine Western culture. Some variants of the conspiracy allege that basically all of modern social liberalism is, in fact, a Communist front group."""
See:
https://rationalwiki.org/wiki/Cultural_Marxism
https://en.wikipedia.org/wiki/Frankfurt_School#Cultural_Marx...