There are a lot of examples of this and the left has had some truly great advocates for free speech. In terms of time period, the Red Scare and Mccarthyism was a time when the left was being heavily censored by the right. The Civil Rights movements as well with MLK during the 1960s and then Frank Kameny in the 1970s trying to get rights for gays.
Other leftist advocates for free speech include Obama, Elenor Roosevelt, and Aryeh Neier are brilliant examples.
What counts as "free speech" tends to be subjective: was MLK pro-free-speech or against it? That depends on whose speech you're considering. I can give even earlier counter-examples with left/right flipped (e.g. abolitionist literature in the south).
My initial point wasn't that it never happened, only to show there were never deliberate, strategic positions on free speech by the left or right- only messy tactical circumstances. Not long before McCarthyism was Japanese internment by a giant of the left: FDR.
Obama famously called someone a "jack-ass" after they exercised their free speech on-stage. He also railed against the Citizens United ruling. Having a binary "for/against free speech" is reductive.
Other leftist advocates for free speech include Obama, Elenor Roosevelt, and Aryeh Neier are brilliant examples.