Fairness, Anti-discrimination and Individual Rights Act of 2023 or FAIR Act of 2023 This bill prohibits the federal government and federally funded entities from discriminating against, or giving preference to, any person or group on the basis of race, color, or national origin with respect to contracts, employment, or other relevant activities. Federal agencies must review and modify their policies to conform with the bill's requirements. The bill also provides a private right of action for violations. The bill defines preference as an advantage of any kind, including quotas, set-asides, numerical goals, timetables, or other numerical objectives.