I remember being taught that both were baaaad growing up, but there seems to be a recent concerted effort to link the two indelibly.  Which seems a bit rich to me.  And kinda weird since, you know, the Soviet Union is now defunct and it seems the time has passed for propaganda and demonization.  Seems like this would be the time to begin to look back and try to understand what happened, why it happened, what can be learned from it.  Also, it seems pointedly aimed at Russia, solely Russia (not countries in which some people collaborated with Russia, not places like Ukraine, not Communist countries that, uhm, still exist, etc.) and at all of Russia, as if it were some monolithic entity collectively responsible for everything that happened.  Also, and this is probably what gets me the most, Nazism required human rights violations, atrocities.  The extermination of ethnic peoples was part and parcel of the ideology.  Atrocities were committed in the name of Communism (as we've also seen them committed in the name of Democracy and Christianity and so on) but were not exactly the cornerstone of the ideology.  I have to struggle to find anything redeeming whatsoever about Nazism (can't) but it's -to me- possible to understand and even appreciate the noble and humane sentiments inherent in Communism.  And even now, I repeatedly hear those who lived under Soviet regime lament the loss of some of aspects of life which seemed more humane than what has replaced it, without nec. calling for a return to those days.  This is so completely lost on Americans.  They hear "Communism" and think "pogroms, gulags, censorship."  Which are in fact things we should condemn.  But that's not exactly the whole story...  

"Pretending that you already know the answer when you don't is not actually very helpful." ~Migeru.

Attitude to the communists did not change much, and when did, became slightly more positive. Consensus is that Russians in XX century suffered more from the Nazis and Anglo-Saxon free marketeers than from the communists.

Say, in Levada poll the question "What October Revolution brought to the people of Russia", "new era in their history" was the opinion of 23% in 1990 and 30% in 2006, "gave impulse of social and economic development" gets 26%/28%, "slowed down their development" is at 18%/16% and "was a catastrophe" for 12%/10%.

communists left the church and religion alone

Do you mean after 1991, or after Stalin, or throughout?

State stopped attempts to eradicate church in 30ies, more or less official truce started in 41 and after the war church was left alone in "don't ask don't tell" style.