Δαφνη Ευτυχια Αρθουρος

Such a response would be begging the question (assuming that the act is not bigoted in order to prove that it isn't). But the accuser may be the one who is actually begging the question (assuming that an action is bigoted in order to prove that the person accused is a bigot). E.g., "You don't like Obama. Not liking Obama is racist. Therefore you're a racist. Q.E.D."

Charges of bigotry, racism, and the like are an area where arbitrary accusations are particularly common, so it's particularly important to look out for circular reasoning on both sides.