Even if Putin’s government enacted this, the Russian Orthodox Church is most likely the instigator and the driving force behind the move. It is not a case of an atheist government trying to ban religion. If it were then the Orthodox Church would be in trouble too. The Orthodox Church in Russia are full of fundamentalists and they appeal to nationalistic (fascist type) voters who are big Putin supporters. It holds a place of special privilege within Russia and with the political classes. The same treatment would be shown to Mormons or Catholics or Hindus if they were ever perceived to be a threat to the Orthodox Church.
I have had many debates with JW’s over the years. I have deconstructed many of their “Watchtower” publications, especially the ones that are anti-science (Evolution is not true) or fussing about the “rise of Atheism”. I have help several of them to see Reason and to de-convert. However I would be the first to defend their right to publish whatever they want to publish and would not censure it.
This has very little, if anything, to do with atheism. It is just plain interfaith Christianity at work.