There is a significant ongoing cultural debate about whether identity is an individualist thing or a collectivist thing.

It's both. There is not an either/or binary, rather there is a both/and interplay.

The remaining question then is what is the mix? How is that decided?

The answer is "It depends." It is complicated -- different people are feel need for either more differentiation or more integration.

But just recognising that the binary is a lie is a good place to start.