When these words are taken out of context, they can be twisted and misunderstood. Jesus is teaching the people how to live in God's family. He is not dismissing the Law. "Do not judge" does not mean people can do anything they want to. The Law still applies. It is not our job to judge. God is the ultimate judge. We are not.
Jesus expects more from His followers. Just before this Jesus said, "Love your enemies." We are told to forgive others and God will forgive us. Christians are told to hold each other accountable, to call the person who is straying back to the Lord and His way. The prophet Nathan held King David accountable for his sins and David repented. Speaking the truth in love, calling a fellow Christian to repent and return to the Lord is not being judgmental. It is how we should live in the family of faith. It is what we should expect when we are straying from the Lord and His way of living.