Parentage is not the relevant issue. Culture is. If you are born in a racist culture, it's nearly impossible to not absorb elements of that. Malcolm Gladwell, who is half black has written quite a bit about how surprised and disturbed he was to discover how much of that he'd taken on as well in his book Blink.
"Indeed, more that 50 per cent of black people also have an unconscious preference for white over black people. It’s the society we live in."