The Trump administration is rolling back the deadline for a key rule on fair housing made into law under President Barack Obama—a change with potentially broad consequences for racial segregation.

The new guidance will give communities until well after 2020 to comply with an Affirmatively Furthering Fair Housing rule put in place two years ago. The Obama-era rule represented a long-awaited effort to give teeth to a federal Civil Rights-era requirement that local governments take active steps to u…