Cultural Marxism.
If I may quote a pretty plausible clarification of what Marxism and Socialism are actually describing.
Socialism is the State controlling the means of production. Marxism is the Worker's state controlling the means of production. National Socialism is the Race State controlling the means of production. Fascism is the Nation-State controlling the means of production.
To contrast those definitions with our modern Capitalism. Capitalism is the Individual's controlling the means of production.
Fundamentally Socialism / Marxist Socialism, collectives all private property (including individual / human rights) into the state. Thereby creating a monopoly on Violence and Production.
Cultural Marxism, therefore, is just a differently defined group seizing to Socialize the people to establish a totalitarian regime.
Hitler's hate for the Jews and his assumption that the Marxist totalitarians are ideologically subverted by the jews, don't change what is stated above. Marxism, Leninism, Stalinism, or Hitler's National Socialism, are simply different totalitarian groups fighting for superiority.
And to directly adress your queston, Yuri Bezmenoph KGB Agent, confirmed active measures of the Soviet Union to inflitrate Universities with their Ideology. A plot to weaken and destiablize the United States. ~1980
PS: If you like to learn what Socialism really looks like, I strongly recommend this documentary, this guy infiltrated the north koran regime for 10 Years -> The Mole: Undercover in North Korea