A quick perusal through history will show that conflicts where one side is censorious and the other is not has basically never happened. Usually the winning side sweeps their misdeeds under the rug afterwards.

See: US behavior towards communists and left wing groups during the Cold War, or censorship during WW1 and WW2. The whole "fire in a crowded theater" trope comes from the unanimous Supreme Court decision upholding the conviction of someone peacefully distributing fliers protesting the draft in WW1[0]. Funny how that one usually doesn't make it into the history books.

0 - Schenck vs. United States. Thankfully no longer good law.

Most people are openly taught about the misdeeds of the McCarthy era in schools and in public discussions. This wasn't swept under the rug, most people agree that it happened and wasn't a good thing.

Eventual recognition of misdeeds is nice, but irrelevant when the original claim is that there is (or has been) one side that’s anti-censorship. Being pro-censorship and then apologizing later isn’t enough.

How much do they learn about the Office of Censorship set up following Pearl Harbour and the role the federal government thought it played in defeating Hitler and Japan? Or the history of battles over "obscenity" laws, often upheld by constitutional courts?

Learning "censorship is unAmerican, here's an example of how we tried it once and it was really bad so we ended it" is the definition of sweeping the nuanced reality of speech battles in the US under the carpet in favour of the free speech version of American exceptionalist myths.