While traditional Marxism embraced an economic struggle between the haves and the have nots, soft Marxism places the conflict in social terms, the majority and the minority. The majority are the privileged and oppressors, the minority are the under-privileged and oppressed.
The Frankfurt School social theorists fled Germany to escape the Nazi regime in the years leading up to WWII and came to America where they took leadership roles in American universities. This explains why the US (ironically, since we fought and won the cold war against the USSR) has become one of the strongest centers of Marxism in the world today. The Social Sciences and Humanities departments of American (and other Western) universities are rife with soft Marxism.
They attacked education (particularly history, Western civ, etc.) through the promotion of a broad approach known as “Critical Theory.” This school of thought can be understood fairly simply as the critique of anything with roots in historically Protestant, Western culture. So “Black Critical Theory” was the study of how white Protestant European culture gave rise to the systemic and institutional oppression of blacks. Feminist Critical Theory focused on how White Protestant European culture gave rise to a dangerous patriarchal society that oppressed women. Over time, various Critical Theory courses replaced the study of American history and Western Civilization, which is now almost completely absent from university curricula.