He told the BBC that he fully upheld the Church's position that the sexual abuse of children was a crime that should be dealt with "according to the requirements of civil criminal law and canon law".
Companies will be able to ask applicants for jobs what their position is on issues such as civil partnerships or sexual counselling for gay couples, and refuse them the post if their religious beliefs would prevent them from doing the work.
But Mr Cain has seen his position as a leading candidate slip in recent weeks after allegations of sexual harassment and a 13-year-long extramarital affair came to light.