Trotsky wrote in the middle of the Civil War: "The censor should protect military secrets. As to the rest, this esteemed office ought to be put in its place." This was not a ritual phrase or a boast. Up until the mid-20's the following anti-Communist authors were published in the Soviet Union: Kadet Pavel Miliukov; Mensheviks Martov, Sukhanov and others; General Denikin; Alexander Kerensky's memoirs; monarchist Shulgin's books and many other historical-political writings by enemies of the October Revolution.
It is true that some newspapers were shut down for publishing outright slanders and calling for rebellion. However, any government does that. Kerensky shut Bolshevik, Anarchist and left-Menshevik newspapers in July 1917. Abraham Lincoln closed pro-secession newspapers during the Civil War.
In the US, France, Great Britain and other bourgeois democratic countries in time of peace a newspaper convicted of slander would be bankrupted in the courts. In time of war, action would be more swift: e.g. in September 1914 the French gov't shut down Clemenceau's "L'Homme Libre"; in 1940, the US gov't arrested the leadership of the SWP for anti-war propaganda. Great Britain did the same with respect to the British Trotskyists in 1944.
Generally speaking, Marxists are against government censorship. We are, after all, for the withering away of any government. Socialism can be brought about only through the conscious action of the world working class. This working class must have the absolute freedom to discuss what it is they are constructing.
Stalinism created a totalitarian state and a machinery for total censorship and for the systematic falsification of history precisely because it was an anti-socialist political force which protected the material privileges of a tiny ruling elite. Its machinery of state censorship was needed to cover up the essentially anti-socialist character of the state and the economy.
With respect to censorship, as in many other matters, Stalinism and Marxism (Trotskyism) are opposites.