Even though, it was produced to inspire national pride and to commemorate the 20th anniversary of the event, Battleship Potemkin is famously known as one of the first propaganda films and was banned not only in its home country, but also in western societies some with free speech rights, however it was still censored.
Perhaps, the reason to why it was banned in western societies was because they were afraid of the ideas it could spread, because the very idea of mutiny was and continues to be threatening to the status quo of the military.
Battleship Potemkin graphically shows how the unlisted men, the muscle of the ship, overtake the officers and administrative personnel. They were angered and pushed over the edge after they discover a side of beef has spoiled, and refuse to eat it. The ship’s doctor inspects the meat, and discovers maggots wiggling on the surface, but just offers the suggestion wash them off. However, this is not good enough for the men because they are tired of the poor conditions on the ship and want to be treated better. The fight begins slow and builds, with the mob mentality taking over.
At one point, the guards are called in and ordered by the officers to shoot and kill their own men who are cornered on the deck. However, the leader of the mutineers asks the impromptu executioners to not shoot, because they are not shooting the enemy, they are shooting their brothers.
Western societies were afraid of the reactions and the repercussions that could take place if this film had been shown at that time; because the idea of taking control from your superiors is very infectious, and by censoring and banning this film from being shown, the government and by extension, the military were containing that very virus. They were preserving and protecting their jobs, and possibly their lives.