It's very hard to make statements about communism "in general". If we start with communism as a theory, it's hard to say that this is true. Communism, in a nutshell, holds that workers of every nation and ethnicity have more in common with one another than with their co-national exploiters, so on this level it is actually extremely supportive of ethnic diversity.

Communism in practice is a different matter. Modern communist theorists usually support diversity, although are somewhat suspicious of it as a distraction from the struggle against capitalism. (This is a broad brush, though) Communist states, especially large multi-ethnic ones like China and the former USSR, were often fronts for imperialism, although it could be argued that this was in spite of communism rather than because of it. (And of course many neo-communists will tell you that these were not genuinely communist states).