I think that is not nearly as certain as you say. Some identities are very very outside the norms of local culture. (For example, I identify non-human, which is quite rare in any part of the world)

Well no two identities are exactly the same. But there is a shared part. It's an intersection.

When the USA hockey team played against Canada after Trump threatened to annex Canada, the Canadians booed the US team. Not because they hated the players, but because they wanted to show that they were pissed. As a response, the US supporters booed the Canadian players. Why? Because they felt attacked "as Americans", not because they supported Trump's idea of militarily invading Canada.

That is a shared identity. And surely in this crowd, not everybody identified as a white heterosexual male.