The Greek word for judge is krino and it means to call into question. This is what Jesus means when He says judge with righteous judgment. We are to call into question the unbiblical actions of individuals and discern for ourselves whether or not to follow such a person. This is something that is sorely lacking in the Christian community today. It seems everyone is afraid of being accused of judging others. Mostly this misrepresentation of scriptures comes from those who are not following Jesus at all, let alone being biblically knowledgeable. When that verse is used it is always in relationship to someone condemning someone elses seemingly judgmental attitude. Christians arent to condemn, but we are to judge/call into question the actions of others and use biblical discernment to do so.
Do not judge according to appearance, but judge with righteous judgment. John 7:24
I Corinthians 2:15 But he that is spiritual judgeth all things, yet he himself is judged of no man.
2 Timothy 4:2 preach the word; be ready in season and out of season; reprove, rebuke, and exhort, with complete patience and teaching.