Personally, I never knew “liberal” was as a derogatory term by the left until after college, when I started reading communists online.

(I did hear “neoliberal” a lot, but that’s quite different, and used much more widely)

Very few people in America seem aware of what the “hard left” is actually like.  The mainstream right does worry about communism, but tends to emphasize (real or imagined) coalitions and unities rather than splits (cf. Horowitz’s “Discover The Networks” site) – they mostly tend to claim that the center left is actually a front for communism, or allied with communism, or some other variant on the idea of a “vast left-wing conspiracy,” with “communism” also assumed to be internally united.

Looking at the other side of the picture: I don’t think the American mainstream left is very aware of divisions on the “hard right” either, and tends to lump everything together as well.  But the “hard right” at least has enough of a presence that the typical Democratic voter learns to distinguish (proverbially) between their non-doctrinaire but very racist grandpa, their fundamentalist homeschooling aunt, and their uncle in the Marines who thinks civilians of all stripes are all weak and could use some military discipline.

Many people know that the left has schisms, at least well enough to laugh at the “People’s Front of Judea” joke, but they still tend to think of all hard-leftists as (1) equally marginal and ignorable, (2) distant and indistinguishable but vaguely “cool” allies, or (3) a united coalition of evil.