If you believe in black and white then you're accepting the core ideology of racism. People are individuals who should be free to act themselves without someone telling them they aren't black enough or white enough. If a "black person" speaks proper English in the US then many in the US will think they are "acting white". This in my opinion is racism. It strips individuality from people and punishes people for being smart in favor of promoting a stereotypical manner.
Race was invented and on a scientific basis it is proven not to exist. So if it does not actually exist it must be a mere social construct. Families exist, genes exist, race does not necessarily mean either of these things. Your race is how other people think of you and where others peg you, while biological family is what you actually are genetically. Learn the history of your family, get a genetic test, and forget about everything you learned about race.