I think you're misunderstanding - "homogeneous" as a cultural description is a spatial metric, not a time metric. Homogeneous cultures indeed change across time, influenced by war and foreign media/languages, just like any culture. The point is not that they do or do not change, the point is that they do so together, largely.

>The country _does_ have a really notable cohesion and shared identity

This, and race/culture, is what is meant when people say Japan is homogeneous compared to other developed nations.