The Neo-Marxist faction of the Left (i.e. those who believe in cultural hegemony, followers of Marcuse, postmodernists etc.) are, by reason of their ideology, almost never supportive of free speech. The trouble is, while once they were a marginal faction of the whole Left, they have now come to dominate certain sections of the Left.
Before the 1960s, Neo-Marxists were very fringe, with ‘the Left’ firmly working class orientated. From the 60s onwards, they were less fringe, but still not mainstream. They only became mainstream post-2012 or so, I think.