Prohibits discrimination on the grounds of race, tribe, place of origin, national or ethnic origin, political opinions, colour, creed or gender with regard to access to public premises or supply of commodity, service, or facility. S. 6 prohibits persons from making statements regarding "racial superiority or hatred" if such statements would endanger the rights, freedoms and reputations of persons in Zimbabwe. S. 10 provides for exceptions to the Act with regard to political and religious organizations, as well as for acts "reasonably justified" in view of physiological differences between genders or in the interest of public morality. Amends the Unlawful Organizations Act (C. 11:13) so as to allow the President to prohibit organizations which propagate racial discrimination. Sets forth penalties for contravention of the Act. Repeals the Public Premises (Prevention of Racial Discrimination) Act (C. 8:12).