It always matters. The fact that you're even asking this shows ignorance of the majority of conflicts in human history. People know exactly what white means. It means European. No, Hispanics are not white. Yes people care. Americans have just been told for decades there is only one opinion they are allowed to voice publicly (often with the threat of impact to their careers). Yes Marxism is the problem.
Discussion
How do we know exactly what people think though? There's millions of people, all with their stories. Not everybody will think the same. Even if we had several referendums, it would take a bunch of them to precisely define what people actually think. Especially when it comes to races because of their inherent subjectivity.
And I'm not trying to be oppositional or conflictive. Everybody is entitled to their perspective. If some people want a white only country, I'm cool with that, that's their thing.
I just think that's not the actual problem. That's the only thing. I think it's deeper than genetics.
I think philosophy and culture is what really matters, not genetics.