I doubt all the Soviet Union and other authoritarian communist regimes censored for decades was hate speech.

Sure, at the moment the left seems to largely align with social liberalism, at least in the west. Maybe authoritarianism is generally more correlated with conservatism, and conservatism with right-wing politics. But left vs. right and authoritarian vs. liberal aren't really the same axis, and it would seem historically quite myopic to think left-wing views somehow confer immunity to abuse of power.