PODs would affect he result. IE Barbarossa is less damaging and US gives lend lease to USSR, Russia takes Italy and Germany, Britain lands in France to prevent a USSR to the English Channel scenario. In this event, the USSR is much stronger and likely the hatred between German and Russian is a lot less, as the Germans did not have the success to start their insane occupation polices against the Russians. (It's hard to get mad at the Germans being cruel to Jews in Eastern Poland when you are a Russian from east of Moscow.) So, this ATL USSR would be an economic powerhouse and likely less cruel. They would be occupying Germany without it being bombed into dust. Italy might get destroyed in the process of "liberation" as it is a peninsula and they will fight.
In this event, the USSR either breaks up sooner (as Europe SSR will be outproducing the Russian SSR from the get go), or the Russians contrive a means of economic extraction that is efficient enough to avoid this, which might leave a USSR in the modern day. We would probably view them as a backward EU of sorts, so transnationalism and one-wordlism won't have the cache that it does today.
As for the Roman Church, it depends upon whether the Italians get defeated decisively before Rome, or if Italy keeps fighting. If it is a quick defeat, then the Pope stays put. Stalin likely won't mess with him as he has many Catholic subjects in Poland, Germany, and Italy and he will want to succesfully attain economic concessions. Stirring the pot on religion isn't going to happen, simply because ATL does not have the crushing, civilization destroying defeats that OTL has.