Sorry, I didn't want to devolve this into a history discussion. I invoked the Nazis not as an example of right wingers, but at the last prominently known book burning during which irreplacable knowledge was lost. Hitler, Stalin and Mao are obviously bad representatives for most (unfortunately not all) of the political spectrum today.

Unless you want to include edgy atheists burning holy books, but that is provocation and not an attempt at censorship.

They are not primarily left. They are authoritarians foremost which use the names of Marx (very much not authoritarian) and Lenin (somewhat authoritarian) concatenated as Marxism-Leninism to justify very much authoritarian systems.