A more relevant way to put it, and the first part of the quote: "Whoever fights monsters should see to it that in the process he does not become a monster."
Stuff like internment camps, crushing dissent at home, and the whole process of disagreement becoming treason.
Well, several updates indicate that the anti-communist laws are going to be challenged, potentially overturned. So this atmosphere of persecution may exist, but it won't last that long.
When we look at governments that have dealt with past atrocities Germany is in many ways the gold standard. Here are some factors that allowed Germany to do so:
1. A strong state that vigorously enforced anti-Nazi laws, making sure that they could never again be a significant force in politics
2. An education system and government that stresses both the atrocities and the culpability of all Germans in them, so that people aren't raised to believe that the Nazis were an aberration that can never happen again.
3. (At least in West Germany) a booming economy, which makes it so that people accept the new state and don't long for the "good old days" of Nazism.
In order to be successful in dealing with the legacy of Stalinism Russia needs the same things, and the question is: can a state ravaged by civil war and political infighting manage to pull this off?
Those are three very important thresholds. To answer the question:
1. The CNS is ruthlessly going to town on the Stalinists, so no doubt they are pushing laws banning the Communist Party.
2. The CNS has kind of started the process: they've let Jews immigrate, and they executed an MGB agent to demonstrate "never again". They also need to make themselves look better, so they'll do everything they can to educate people about the atrocities. Textbooks, memorials to victims of the Soviets, from kulaks to Abkhazians
3. The potential for Russia's new leaders to be oligarchical kleptocrats is a lot less than OTL. The oligarchs were former communist officials (again proving the utter lie of Soviet ideology). Many of these venal fellows are well, going to end up with bullets between the eyes. So it is more likely Russia's new leaders will use the aid money they get to rebuild instead of line their pockets.