Well, for one concrete example in the UK, it made Animal Farm a lot harder to publish: the work was an obvious attack on a brave and loyal ally, so George Orwell had four publishers refuse to publish it at all, then one agreed only to backtrack after the Ministry of Information warned them against it.

TS Eliot also gave the book lukewarm praise, and argued that the pigs were in fact the best suited to run the farm.

So there was at least an atmosphere when even caricatured criticism of communism was looked on with strong disfavor.

Throughout World War II, US propaganda portrayed Stalin in a positive light.

Did it? I can't recall having seen any examples of US-produced propaganda posters that were pro-Stalin. Mission to Moscow was made during the period, but it was a commercial flop. I think it would be more accurate to describe US propaganda towards Stalin during the time as "neutral".