English Standard Version (ESV)
What separates us from God is our sin -- in all of its forms, although we often like to pick and choose certain ones. Sin separates us, and so in Christ, we are forgiven and redeemed, restored into right relationship with God. Paul rightly urges us to seek to live in this new status, seeking God in all we do.
What separates us from others is also sin. Our broken relationship with God echoes into our broken relationships with one another. It's little things, like selfishness and anger, and also bigger things, like racism and discrimination -- these separate us. However, Christ comes for all, and is seeking to restore us to one community as well. This is why Christ spends so much energy breaking boundaries, reaching out to include others in the community of faith. The Pharisees are often furious at the ways Christ does this, but Christ has come to restore us to God and to one another. Therefore, just as we seek to live a life faithful to God, let us live a life faithful to one another another, always seeking to serve.