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In the 1960s/1970s the left had complete free speech on campuses. It was perfectly acceptable to be a Maoist. Real leftists like Chomsky have never been de-platformed. I'm curious to know what the right effectively suppressed in 1980-2010, which is the time frame you mention. Those were pretty free decades. I do not recall censorship. Also, the current "left" is not really left outside of cultural wedge issues. They…
In the 1960/70s (when my parents were in college), it was perfectly acceptable to throw a milkshake at a fellow black student with literally no consequence. It was necessary for black male students to walk with black female students because of harassment. I know this because it was literally what my parents had to deal with.
So "complete" free speech is a resoundingly absurd idea, in no way were they protected and able to speak freely. As I mentioned above, the suppression (true, I wouldn't say censorship) resulted in a sort of de-facto very unfree speech.