What PODs (Preferably after 1789) would be needed to make the races be equal to each other in the united states of america, by the year 1900.
After 1789... that's harder.
Two pre-1789 possibilities:
1) A decision that British law applies in the Colonies, and that since there is no positive British law establishing slavery, slavery cannot exist in the British colonies. The colonists replace chattel slavery with perpetual indentures, but the system gradually declines over time.
2) A decision by the Constitutional Convention to decree the eventual end of slavery; perhaps by a clause stating that slavery will no longer be hereditary.
A third pre-1789 possibility: the Confederation Congress bans slavery in all western territories, not just the Northwest (this move failed by one vote OTL).
A post-1789 ruling by the Supreme Court that hereditary slavery violates the Fifth Amendment (deprivation of liberty without due process).
All of these PoDs mean that slavery is not entrenched in the U.S. that in fact the eventual end of slavery has been accepted by everyone.
Racism in the U.S. developed as a conscious ideology in the late 18th and early 19th century, as a defense of slavery. Without the need to defend slavery, the need for racial ideology goes away.
Racial bigotry and discrimination, and legal inequality persist for decades, but agitation against this invidious practice begins in the early 1800s, and by 1900 has succeeded. If that seems unlikely - remember that racial discrimination conflicts with, and racial equality conforms with, the founding ideals of the U.S.
Nominal legal equality of races was established OTL with the Reconstruction Amendments in 1865-1870. ATL, a similar result could be achieved by the 1880s, with general acceptance, and resistance generally dying out by 1900.