The USSR stopped listening to guys in robes and started exterminating them, especially in 1920-1930s. It also can boast of ethnic cleansings (= removing whole nations from their homes) and slaughtering the dissident. So moving away from religion doesn't automatically make a society more tolerant.
I don't think Khazakhstan is a good example, because after the collapse of the USSR there were ethnic tensions between the Turkic and the Slavic communities which eventually made thousands of the latter leave the country for Russia and Ukraine.
Now such things are not heard about any more, yet in case Russia (Zhirinovsky already does it on occasion) propels its interest ethnic tensions (possibly with a religious admixture - if ISIS takes a hand) will be awake in no time.
Bookmarks