Globalization introduces a wider flow to goods and people, but it absolutely does not mean that geographically-distant cultures will assimilate to each other. As per inevitability, neither will adjacent cultures by default. If you look at Western soft power, you will see that consumption of cultural products is not anywhere close to related to assimilation.

Unless you have a one-world government that continuously and uniformly redistributes populations around the world for the purposes of cohabitation and breeding...

But let's leave out this planet and activities thereon, and consider that other science fiction trope of interstellar colonization. Would cultures of planets assimilate? How? By my notion of "way of life"? In what sense that doesn't assume identical worlds or standards for settlement? Let's be honest, here or there or anywhere, even communication reliant upon teleportation technology would not suddenly replace the existing social logics.