I think it depends on the culture in which one is raised. I'm partly Filipino, but I was not raised in the Filipino culture and don't know the customs or holidays or languages. Same with my Chinese, American Indian, and Spanish heritages. I'm also partly Welsh and Irish and Scots, but no one looking at me would likely see that.
I was raised a Californian, more than anything else, I think. And my experience traveling around this country and the world, being Californian is perceived as almost a racial identity.
Sometimes racial identity is pegged to who you're with. As a child whose family made frequent moves, it was important that I fit in as soon as possible. Sometimes I did this by identifying with a majority race, sometimes by setting myself apart as an "exotic" minority race. For a large part of my childhood, however, I lived in low-income areas that were predominantly black, which is not in my racial heritage. In these communities I was identified by others as white, a racial identification I have never really been comfortable with.
These days, I prefer to check the "other" box and if asked for a clarification, enter my name.
Humans are animals who prefer to gather in groups of like interests and the group you choose to belong to can depend a lot on what interest is being addressed as well as where you are welcomed.