The law is Title VIII of the Civil Rights Act of 1968. Fair housing bills had stalled in Congress for two years, and the Kerner Commission had warned in early 1968 that the nation was moving toward two societies, one Black and one white. King's assassination on April 4 and the uprisings that followed pushed Congress to act.
The act outlawed redlining, discriminatory advertising and refusals to rent or sell based on race. It also requires federal agencies to affirmatively further fair housing, meaning they must work to undo segregation, not only avoid discrimination. In Texas Department of Housing v. Inclusive Communities Project in 2015, the Supreme Court held that policies with discriminatory effects can violate the act even without proof of intent.
Enforcement has been weak. The Urban Institute found that the 30-point gap between Black and white homeownership rates in 2019 was wider than the 27-point gap in 1960, when housing discrimination was still legal.