Jarvis Williams has written a helpful book explaining what Paul taught about racial reconciliation. What I have found especially insightful is the distinction he makes between ethnic diversity and racial reconciliation. While, of course, there is much more, the following quote provides a taste:

"Ethnic diversity only means that people from various backgrounds worship, work, or live in the same environment. To the contrary, racial reconciliation means that different races are now members of the same spiritual family by their faith in Christ because of his death for sin, and they have equal access to God by the same Spirit since Jesus recreated all who believe into one new man. This new man is the new race in Christ. This new race transcends our old ethnic identities and our old man in Adam (see Rom 6:6). Thus, regardless of whether a church, a community, or a work environment is ethnically diverse, racial reconciliation can still be a reality, that is, if ethnic diversity is not absent in those environments because of racist ideologies. Racial reconciliation can still be a reality when the members in those environments demonstrate the same type of selfless and Christlike love to believers from different races as they would those believers from their own race and when they universally pray for and minister to their brothers and sisters in Christ in their communities and in the world regardless of ethnic distinctions. Indeed, Paul’s gospel calls for a mixing and inclusion of different races in the church (i.e., ethnic diversity [see Gal 3:28]), but it especially calls for Jews and Gentiles to live with one another in love as God’s family even if a church might not be able to be ethnically diverse because everyone in the community is from the same homogeneous unit. Practicing racial reconciliation means that I regard a white Christian as my brother (remember that I am an African-American), but not an African-American who is a non-Christian. Hence, my love and service to my Christian brothers and sisters should transcend any love, affection, favoritism, devotion, and service that I offer someone from my race, because Christians are part of the family of God. Membership in the Christian family is much more important than association with any ethnic group or club. Churches that are located in ethnically diverse communities should reach out to those ethnic groups in their communities, and churches that are not located in diverse communities should think of and pray about practical ways by which they can live out the reconciling power of the gospel both in their community and throughout the world."

Jarvis Williams. One New Man: The Cross and Racial Reconciliation in Pauline Theology