Jesus was a good example of this. He ministered to men with leprosy, a man filled with demons, a woman living in adultery, a tax collector.
Jesus commanded the Jews (in Acts 1:8) to witness to the Samaritans. However, they weren't anxious about obeying Him, because they had racial prejudices towards the Samaritans. Plus, they knew that the Samaritans hated them. Philip is the first man, that we know of, that obeyed Him. When other Jews were fleeing Saul's persecution, Philip went to Samaria. He spoke to the people and God used him to heal people who were lame, paralyzed, and filled with evil spirits. (Acts 8:3-8) The Samaritans were happy about the miracles they saw and revival started to break out.
The Lord tells us to go and make disciples of all nations. He doesn't exclude the people that we don't like. When we obey Him, lives are changed for eternity. People who are different and alone, will feel comforted knowing that a Christian reached out to them.
Christ loved us, and died on the cross for us - knowing that we were sinners, rebellious, and had nothing to offer Him.
Let's challenge ourselves to reach out to people who make us feel uncomfortable. Can you think of anyone?