One of the best illustrations of what Jesus meant when he said to love our enemies is the Parable of the Good Samaritan (Luke 10:25-37). In this familiar story, a man is mugged on his way down from Jerusalem to Jericho. Both a priest and a Levite pass by him without helping. Finally, a Samaritan stops and helps the man, giving him medical attention, taking him somewhere safe, and paying for his recovery.
Jesus tells this story in the context of the question, "Who is my neighbor?" The lawyer type is apparently thinking in the same vein as Matthew 5:43: love your neighbor and hate your enemy. So he is willing to love his friends but perhaps wanting to exclude his enemies from those toward which he must show love. He sounds like he wants to be clever. "Ah, but who is my neighbor?"
Jesus' answer is topsy-turvy. First, he does not tell a story about someone helping a Samaritan, although in effect Jesus' answer is that Samaritans are his neighbors. But the story honors the Samaritan as the one who actually fulfills what God expects. Meanwhile, those like the lawyer--the priest and Levite--do not.
Samaritans were of course hated by many Jews at the time. They lived in the region between Galilee, where Jesus lived, and Judea, where Jerusalem was. While Galilee in the north had largely turned to follow the religious approach of the south in Jerusalem, Samaria remained both politically and religiously distinct. Samaria had a long history of resisting the advancement of Judea, and they had their own version of the Jewish Law that did not see the temple in Jerusalem as the legitimate temple. They had their own temple much of the time. They also tended not to worship Yahweh exclusively but to mix worship of him with other gods in the world like Zeus.
So for Jesus to make the Samaritan the good guy would have been grating, to say the least. Any lawyer of this sort would surely have found it insulting. What's even more subversive is the situation that Jesus creates. A priest or Levite would surely have wanted to avoid the mugged man for purity reasons. He would have been bloody, and contact with blood of this sort would make a person unclean, and purity was a major concern for a priest, whether they had just finished their priestly duties or not.
Some try to soften the startling nature of what Jesus is saying here by pointing out that the priest and Levite were headed away from Jerusalem. If they were working in the temple, they were done for the day. It is hard to know how significant the direction of travel is in the story. It does not change the fact that Jesus did not put a Pharisee in the story as the one who avoids the mugged man. Jesus chose two people for whom purity was a concern because of the Old Testament laws.
In other words, this is another story like the one where Jesus gets into conflict with Pharisees over his disciples picking heads of grain on the Sabbath. It is another story where he implies that people trump rules for their own sake, in this case a priestly concern for purity. Loving our neighbor or enemy takes priority over lesser laws and concerns.
Once again, we find that Jesus leaves no excuse for hating our enemy. When we have a concrete opportunity to help others in need, we'd better have a very good reason not to do it. Jesus does not show himself to be an "absolutist" in these stories. Quite the contrary! He regularly makes exceptions to the rules, even breaks the rules, when loving others is at stake.