This is not true, both because it’s not the only one[1], and because the constitution hasn’t prevented state censorship in the US[2-4].
> It protects us from governments like the UK that don't think they have any limits to control their citizens.
How would it do that? The US constitution has no power over the UK.
[1]: https://worldpopulationreview.com/country-rankings/countries...
[2]: https://journals.ala.org/index.php/jifp/article/view/7208/10...
[3]: https://historycollection.com/10-situations-in-history-when-...
[4]: https://en.m.wikipedia.org/wiki/Censorship_in_the_United_Sta...