I can talk about forms of acceptable dress for soviet and eastern European socialist politicians, but I can't say much about eastern communism, so I won't be answering this question in regards to China, the DPRK, Vietnam, or any other socialist states in the eastern hemisphere.

The answer is relatively short: were 'western' style suits ever banned? No, they were not, and communist leaders often gladly wore suits. The biggest style difference in contrast to the west, especially pre-war: instead of top hats, an almost cartoonish feature of the bourgeoisie, socialist politicians usually wore characteristically working class hats, for example fedoras. This remained in fashion until the fall of the USSR.

But back to the question at hand. Suits were worn often and by many. Most non-military members of the soviet government wore suits, while military persons wore something like a uniform. Prior to the second world War, this was notably similar to Stalin's simple military fatigues, but later evolved to be a dark blue suit with medals and decorated shoulders and collar.

Stalin personally established his style that you are referencing as not more than a reflection of how he wanted to be seen: simple, ordinary, somewhat militaristic. He later advanced this into a more decorated white uniform, which then became his preferred clothing in public for the rest of his life.

As for eastern Europe, suits were still the most common form of dress for politicians, though some individual leaders, primarily those with military backgrounds such as Josip Tito and Wojciech Jaruzelski, often appeared in military uniforms. European communism never opposed suits.