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Many of the later efforts to support local cultures in the USSR were pretty good but were ultimately hindered by the fundamental paradigm of Marxism-Leninism with all its lies and double-think.
So basically you could engage in local culture as much as it didn't step out of the boundaries set by the party line at given moment, which gradually narrowed down, peaking during Stalinism.
Ultimately, in 80's everyone had enough of everyone so much that they just ran away.