It's worth noting that American censorship in, say, 1960, was at close to the same level.
See: https://en.wikipedia.org/wiki/Film_censorship_in_the_United_...
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See: https://en.wikipedia.org/wiki/Film_censorship_in_the_United_...
(reading that again I discovered https://en.wikipedia.org/wiki/Mutual_Film_Corp._v._Industria... ; the idea that movies were not counted as free speech for several decades in the US may come as a surprise to other HN readers)
The argument wasn't even made that it was a violation of the first amendment (which would have only applied to laws by Congress, not states). The argument was more about things like whether it was a violation of interstate commerce to have to have different versions of a movie for different states. They did argue that it violated the Ohio state constitutional right to free speech.