Sorry if you're that nostalgic, but the cold war ended decades ago.

You're right.

https://en.wikipedia.org/wiki/And_you_are_lynching_Negroes

Use of the phrases like these, exemplifying the tu quoque logical fallacy, was an attempt to deflect criticism of the Soviet Union by referring to racial discrimination and lynching in the United States.

Look at it from the other angle. If you are to blame someone for doing XYZ I assume that you are sparkling clean. If however you are doing the same thing simply get lost. You have no moral right to blame someone for doing exactly the same thing you do.

It is not "Classic Chinese / Soviet tactic (TM)". It is a friggin natural sense of justice that normal people possess.