Germany has never had much of a culture of free speech.
The intelligence agencies in charge of monitoring extremists have long had their own problems with extremism. The former head of the agency for "Protection of the Constitution" ("Verfassungsschutz") himself turned out to be a xenophobic right-wing extremist.[0] They have wide authority to spy on citizens based purely on their political views. Unless you really, really trust the agency doing that, this is not a good thing for society.
During the war in Gaza, the various restrictions on free speech were used to crack down on pro-Palestinian protesters. For many months after October 7th, many cities (such as Hamburg) issued blanket bans of pro-Palestinian protests. A Jewish German woman was even arrested for standing alone in a public square and holding up a sign about Gaza, because that was supposedly a violation of the ban on protests about Gaza.[1] All sorts of people have been banned from entering the country (including an elected member of the European Parliament, Yannis Varoufakis [2]), purely because of their views on Gaza. A major conference in Berlin was broken up by police because they allowed "banned" individuals to speak over Zoom (banned explicitly for their views on Gaza) [3]. When there's a major event going on in the world (which your government is involved in), and the government tells you you're not allowed to demonstrate about it, that's not a good thing.
These supposed protections have not done much of anything to prevent the rise of the far right in Germany. The "Alternative for Germany" (AfD) is a right-wing extremist party filled with "former" neo-Nazis (such as the leader of the party in the state of Thuringia, who used to write neo-Nazi articles under a pseudonym [4]). The AfD is now polling at 25%, making it tied for the most popular party in Germany. Even if the AfD doesn't get into government, the conservatives are imitating them more and more. The Chancellor recently said that German cities no longer look right (because you see too many foreigners). When asked what he meant, he responded, "Ask your daughter" (with the obvious implication). And no, the agency for protection of the constitution is obviously not going to tell him to stop saying things like this.
The German system of political censorship is not something that other countries should be imitating.
0. https://en.wikipedia.org/wiki/Hans-Georg_Maa%C3%9Fen
1. https://www.aljazeera.com/news/2024/4/1/we-jews-are-just-arr...
2. https://www.newstatesman.com/diary/2024/04/cancelled-germany...
3. https://de.wikipedia.org/wiki/Pal%C3%A4stina-Kongress_in_Ber...
4. https://de.wikipedia.org/wiki/Bj%C3%B6rn_H%C3%B6cke#Pseudony...