This essay provides a highly thought-provoking answer:
https://quillette.com/2020/08/16/the-challenge-of-marxism/
The argument is sophisticated and hard to summarise, but essentially, the author argues that "enlightenment liberalism" (i.e. the sort of philosophy that dominates universities) has a flaw at its centre that both creates Marxists and causes "enlightenment liberals" to constantly give in to the demands of those Marxists. The cycle goes like this:
1. Liberals assert that henceforth all with be free and equal, and that these things are self-evidently desirable (i.e. using reason alone).
2. Some liberals observe that life is full of inequalities and lack of freedoms. Because everyone is supposed to have equal opportunities, and because liberalism is generally uninterested in historical or traditional justifications for things, unequal outcomes demand an explanation which they find in the assumption of oppressive hierarchies. These liberals become Marxists.
3. They demand affirmative actions be taken in order to rectify these supposed oppressions. Embarrassed by the existence of inequality and lack of freedoms after declaring that their society is meant to have neither, liberals agree to these demands.
4. Realising they got what they wanted with little resistance, and that inequalities and lack of freedoms still exist, Marxists return to step 1.
In this framework the cause is nothing as simple or skin-deep as bad PR or lawsuits. Perhaps fear of those does play a role, but the author argues that the core reason is that the university is staffed by people who are genuinely embarrassed and upset by Marxist critique. Lacking intellectual ammo or a coherent philosophy of inequality, they invariably cave in when faced with outspoken demands that appear to align with their own agenda of equality.