When Barack Obama first emerged as a presidential candidate, I thought of his ethnicity similarly: With a black father and a white mother, he's biracial, equal parts "black" and "white".
What I saw during his presidency, though, was that a significant number of white American citizens were treating him as black, in the negative sense of "he's not one of us", "it's scandalous that a person like him should have power over white people", birther nonsense, etc. If your country is treating you according to the one-drop rule, and has been treating you this way for much of your life, then that's a particular experience you're living, and that experience is different from my life experience as a person with no recent African ancestry.
I'm not surprised that Cuban culture is different on this. Good for them.