You've apparently never read the Acts of the Apostles š. You should give it a try. Hint: It's in the New Testament. I'm not sure what True Communism was, but a lot of stuff in Acts sure sounds like it: All property and income was pooled, the poor and windows to be looked after and (eventually) the faith was to be spread to new ones (although not by coercion, I give them that credit.)
I tend agree with you upon Communism and Catholicism being incompatible belief systems, which makes the following observation all the more interesting:
It's a historical fact that Christianity as it developed bears almost no resemblance to what is expressly told in the Gospels, Acts and the rest of the official Bible. There is plenty of (non-Church) criticism available. The one I'm most familiar with is Nietzsche. In a few sentences: he asserts that the primitive Christianity (pre-Paul) was seized upon by St. Paul, who added aspects of [Neo-]Platonic philosophy as well as some of the "pagan" religions then popular in that part of the world, to make the new Christianity more appealing to the masses.
"Was Paul crucified for you?" writes St. Paul (1 Cor 1:13) Certainly not, but he beyond doubt wrote some of the New Testament and is believed to have written more. But the result, even the early Church, bears but slight resemblance to what the wandering carpenter from Nazareth taught.