The OT law also made legal provision for divorce, yet Jesus said that was put in there out of the hardness of human hearts.
I would describe the slavery situation, especially in the NT, as one akin to tolerance of an existing institution, and not one of endorsement.
Taking the idea behind Jesus' words on divorce in the Law, and applying them to slavery, would also make it a provisional arrangement in light of a flawed humanity that wasn't ready for universal manumission.
Remember, in the US it was in Christian churches that the Abolitionist movement was born, and the idea traces its roots to a Colonial era Catholic priest. The equal rights movement was Christian also. MLK himself was a Christian minister, and couched his language in religious terms.
BTS