I think Gibson is correct to refuse to allow his family into any public discussion. I would do the same. My Dad has some problems, but I certainly wouldn't speak negatively about him publicly no matter what the pressure.
Gibson should not be judged by what his father or any of his family believe IMO.
He told Diane Sawyer, in a 2005 interview, that "my father never lied to me."
Since his father denies the Holocaust and holds the Jews in contempt, it is fair game to ask him if he holds the same views, or if he believes in the truth of them.