Now think of Jesus. He looked at the leper, full of disease, limbs falling off and he embraced that man and said, "Be clean." Jesus wasn't talking just about healing, he was saying that the man was no longer disgusting-- he was embraceable.
Consider Jesus embracing the person you find most disgusting, because he does. Jesus doesn't see that person as someone to avoid, but as the image of God.
Now we are in Jesus' place. If Jesus allowed his betrayer to kiss him, if Jesus prayed for those who killed him, if Jesus ate with the worst of sinners, then so should we who follow Jesus.
Embrace the unembracable.