Race DOES matter in the way people identify themselves, how they are perceived by others, how they interact and relate to other people, and their access to opportunities and resources. Race is real because people perceive it as real, and it affects the way they see themselves and others. Race is a double-edged sword. It may be important for self-identity, but can also be the basis for racism and discrimination. People always define themselves in relation to other people who are seen as different from them.
Race never exists in a vacuum.
Historically the US has conceived race in terms of the dichotomy white-black because of its particular history of colonization and slavery where races were kept separate and were unequal in their access to wealth and power. In Brazil, where slavery coexisted with much intermarriage there is no notion of hypo descent. The exception would be cases like Pele who is no longer considered dark because of his prestige. Although the black-white dichotomy is absent, lighter skin is still associated with higher prestige and wealth while darker skin is associated with lower prestige and wealth. Because US popular culture uses race and ethnicity interchangeably to mean the same thing.