Summary: Anyone as intelligent, individualistic, and morally sensitive as Kolmogorov would obviously have seen through the lies of his government, and been horrified by its brutality. So then why did he utter nary a word in public against what was happening?
As far as I can tell, the answer is simply: because Kolmogorov knew better than to pick fights he couldn’t win. He judged that he could best serve the cause of truth by building up an enclosed little bubble of truth, and protecting that bubble from interference by the Soviet system
It seems likely that in every culture, there have been truths, which moreover everyone knows to be true on some level, but which are so corrosive to the culture’s moral self-conception that one can’t assert them, or even entertain them seriously, without (in the best case) being ostracized for the rest of one’s life.
What’s the inner psychology of the authorities? I think that most authorities simply internalize the ruling ideology so deeply that they equate dissent with sin. Someone who’s arrived at that point is completely insulated from argument: absent some crisis that makes them reevaluate their entire life, there’s no sense in even trying.
Instead the iconoclast can choose what I think of as the Kolmogorov option. This is where you build up fortresses of truth in places the ideological authorities don’t particularly understand or care about [and] wait for a moment when, because of social tectonic shifts beyond your control, the ruling ideology has become fragile enough that truth-tellers acting in concert really can bring it down.
This blog post came out a few days after a male employee at Google was fired for an essay arguing against some(?) of Google's written and unwritten diversity-related rules.