I don't see any connection between the Corleones and communism. I might see it more like fascism, or dirty capitalism - GF1 begins with "I believe in America." GF themes are mostly based on reallife. And the reallife mob was in Cuba and controlled gambling before Castro kicked them out. Expanding to Cuba was a logical choice for a mob family that controlled gambling in the 1950s.


Interesingly, one of the deleted scenes in GF1 DVD seems to show Michael and his bodyguards in Italy passing by pro-communist demonstration. So perhaps they wanted to expunge extraneous references to Communism?

Finally, in GF2 during the Pentangeli and Hagen prison yard walk scene, Pentangeli does compare the family to the Roman empire. So that's a closer comparison - "after all, we are not communists."