Are there any shows that got abruptly cancelled because the government didn't like something they said or did?
Not because of the acting or even the political beliefs of the actors, but because something that was said in front of the camera offended a government agent who got the show axed.
The Austrian show Gute Nacht Österreich. It was the same concept as Last Week Tonight or the Late Show. Well, they did a show about then right wing populist Chancellor Sebastian Kurz' networks and connections. The topic of the show had been announced a day before, but they had suddenly shown a different one, apparently due to pressure from the upper management of the public broadcast.
Only due to massive public pressure could they show it the following week and afterwards their show mysteriously didn't get renewed due to budget cuts, despite being very popular.
They had only come back later after Kurz was ousted because of a corruption scandal
The closest I can think of in the U.S.. was the Smothers Brothers. They were cancelled by the network, not the government, even though they were very popular . They frequently criticized the Vietnam war and government officials.
Not the Government but in Australia in the early 90's we had a one off special of Funniest home videos called Australia’s naughtiest home videos which was pulled off air mid show by the network owner Kerry Packer.
You're not going to find a lot of anything like that.
Either places have little censorship and you can just get a show cancelled without a significant burden of proof, or censorship is setup such that you have to get permission for your broadcast before it airs.
I feel like Mark Thomas on Channel 4 was pretty close to this. He seemed to be cancelled and forgotten pretty quickly but still tours. Was hugely anti-establishment.
One of the musical numbers in the broadway production of 1776 (Cool, Cool, Considerate Men) was removed from the movie release at the direct request of Richard Nixon. The mot recent release of the movie reinstated it.
A few Australian shows mentioned, but one that shamefully hot abruptly cancelled in the 90's was John Safran's
Master Chef / Media Tycoon, because a current affairs host Ray Martin couldn't take a touch of his own medicine and phoned up the ABC to have it pulled.
On the opposite of this, the Stanley Kubrick movie Spartacus (1960) was in danger of being pulled during the Hollywood Blacklist phase when Dalton Trumbo was revealed to be the screenwriter, but President John F. Kennedy went to watch the movie in theaters and publicly endorsed it afterward, helping to end the Hollywood Blacklist as a result.
If this happened in the United States, your best bets are searching around 2001 (iirc, Bill Maher's show at the time might fit your parameters; a revival of Sondheim's "Assassins" was nixed around that time as well) and the early-mid 1950s (around the McCarthy Hearings).