The US is a racist society: "race" has no valid biological basis, but is a salient social category which impacts social and economic interactions in a wide variety of ways, producing inequalities of privilege and injustice.
Whether or not you have bigotry in your heart is beside the point—no one can know such things. When you spend all your energy trying to prove that you are untainted and innocent of racism, it seems like you are missing the point: in a pervasivly racist society, discriminatory behaviors creep in the subconscious of everyone, black/white/antiracist/whatever, and we have to consciously struggle with them. The question is really more about how you interact with broader society racism, not whether you are a naif.