I would just note that anti-discrimination laws, such as in regard to public accommodations and employment, do not make the unlawfulness of the act contingent upon the race, ethnicity, religion, sex, sexual orientation, non-disability, etc., of the person who is doing the discriminatory act. These laws make it equally illegal for African Americans to discriminate on the basis of race, for Muslims and Jews to discriminate on the basis of religion, for women to can discriminate on the basis of sex, for gay people to discriminate on the basis of sexual orientation, etc., etc.
Thus, insofar as discriminatory acts are expressions of racism or sexism, members of those traditionally oppressed groups can be racist or sexist (or even both).