Or if everyone was fine with cultural heterogeneity. You just have to agree on one of these.

What is cultural homogeneity?

Closer to an ethnostate.

I think that's the correct term. I don't think there's such a thing as cultural homogeneity. If ethnic japanese start doing weird stuff as judged by "japanese culture", this weird stuff will immediately be considered "japanese culture", thus making "japanese culture" impossible to define precisely.