Luke 6: “But I say to you who hear, Love your enemies, do good to those who hate you,  bless those who curse you, pray for those who abuse you.  To one who strikes you on the cheek, offer the other also, and from one who takes away your cloak do not withhold your tunic either.  Give to everyone who begs from you, and from one who takes away your goods do not demand them back.  And as you wish that others would do to you, do so to them.
These verses are directed at individuals as they seek to live a God pleasing life in response to the grace of God lavished on them in Christ. This comes across particularly strongly in the Sermon on the Mount in Matthew 5 – 7 where Jesus preached very similar things.
Living like this does not cause you to have a right standing before God. We are saved by grace through faith. Period.
What Jesus is saying here are some of the ways that grace received and believed will demonstrate itself in the life of the believer. These characteristics are also not directed to churches, governments, homes. They are directed to individual believers. This is crucially important to comprehend or the church will end up promoting godlessness and anarchy.
Governments are ordained by God to punish evil doers (Romans 13:1-7). It is not for the governing authorities to turn the other cheek and simply allow evil men to prosper under its authority. Parents are obligated by God to correct their children (Ephesians 6:1-4) and one of the chief responsibilities of a congregation of God’s people is to discipline its members (Matthew 18:15-18; I Corinthians 5:12-13). A police officer, parent, soldier, acting on behalf of his or her authority not only has the right, he has the obligation to use the power granted to him by God for the good of those he works for. Governments are under a command from God to punish evil doers. For a government not to punish evil on the basis of turning the other cheek would be a great twisting of the Scriptures that would only result in evil being given far too much ground. It is crucial to know who Jesus is speaking to if we are going to understand this difficult text properly.