Germany is also one of those countries that blanket bans particular groups/parties in general, which the US didn't really do until after 9/11. Banning a group chat isn't much different.
Avocadolf's channels are public, you could access them on the Telegram web UI even without an account. The German government has tried to get the channel shut down for months now, after Hildmann fled the country and engaged in Holocaust denial (which is a crime here).
The problem is that unlike all other major social networks, Telegram refuses to comply with German laws (in particular the NetzDG) and has refused to name a contact person for the authorities so that egregious violations could be stopped. I read an article that claimed the only form of contact between German authorities and Telegram used to be a bilateral anti-terror coordination with the US FBI, which makes sense given the common problem of radical Islamist terrorism.
So yeah.
My guess is that at this point Germany is saying that this could fall into the criminal side of things, at which point Telegram would care.
Not sure where telegram is registered, but can a foreign company have a criminal responsiblity by just being accessible in that country? I'm sure most of the internet violates some kind of ancient anti-something law, be it nudity or whatever, but noone really cares if boobs are illegal in afghanistan, why care if something is illegal in germany, if you're an (eg.) british company?
Porn sites are probably against the law in Saudi Arabia, but why is that Pornhubs problem?
On the other hand, forcibly removing content for the sake of the content is censorship. It can be censorship that most people approve of - which they usually do when the content is sufficiently vile and irredeemable - but it's still censorship.
And yes, content was censored on. But not only death threats were censored but also holocaust denial, eugenics and inciting hatred against ethnic groups (Jewish groups, specifically).
People on the blocked Telegram channels have denied the Holocaust (including the channel operator himself) which is a crime in Germany, Austria and 16 other European countries [1] or called for the murder, disfigurement or other injuries to politicians [2].
"Anti-mandate discussions" are bad enough, but unlike what went on in Hildmann's channels this stuff isn't criminal so the comparison of yours is a bit wrong.
[1] https://de.wikipedia.org/wiki/Gesetze_gegen_Holocaustleugnun...
[2] https://www.faz.net/aktuell/feuilleton/medien/hunderte-morda...
If they don't go down the route of implementing a state-level firewall such as China is doing, they're fighting a losing battle. And frankly, if Telegram were inaccessible from Germany, the same people would simply use the next messaging app. There's nothing groundbreaking within Telegram that cannot be replicated.
IMHO, this is the government embarrassing themselves with the fact that they've lost the goodwill of a huge chunk of the population and trying to blame Telegram for it - as if the mindset and communication of those unsatisfied people would simply change/disappear if they were no longer able to access Telegram. Which furthermore shows that today's governments still do not understand the internet.
For what it's worth, the NRW Landesmedienanstalt is busy establishing a DNS-level censorship infrastructure against Pornhub, Youporn, MyDirtyHobby and others [1]. It won't take long until providers will be forced to also add Telegram's infrastructure to that list.
[1]: https://www.spiegel.de/netzwelt/web/landesmedienanstalt-kann...
You make it sound like Germany is constantly banning political parties. There have been exactly two bans of political parties in the post-war history of Germany: A nazi party in 1952 and a communist party in 1956. Also don't forget who occupied Germany in this decade and made a lot of its decisions.
Gang injunctions (sufficiently, but not exclusively) prove that this is not true.
(I wish I was joking.)