Matthew 7:1 is indeed a misused and misunderstood verse. Usually when people use, “Judge not lest you be judged”, they mean people shouldn’t be judged negatively. Basically we should not say anything that offends.
Jesus did not imply that anything goes and we shouldn't rebuke or correct anyone. If we read Matthew 7:1-5 we can understand better what Jesus was saying. "Judge not, that you be not judged. For with what judgment you judge, you will be judged; and with the measure you use, it will be measured back to you. And why do you look at the speck in your brother’s eye, but do not consider the plank in your own eye? Or how can you say to your brother, ‘Let me remove the speck from your eye’; and look, a plank is in your own eye? Hypocrite! First remove the plank from your own eye, and then you will see clearly to remove the speck from your brother’s eye." What Jesus was talking about is about people being hypocritical and acting as though they are superior spiritually. Measuring one’s righteousness against another is forbidden by Christ (Matthew 6:1, 23:2-7). Also what is a person's motive for the judgement? Is it coming from a genuine desire to help someone else?
All throughout the Bible and history God's people make judgements. They called/call out sin and called/call God's people to repentance. As Christians we need to make judgements. We have to be able to tell the difference between right and wrong and be willing to call sin what it is. John the Baptist called out king Herod for his sin, Martin Luther “judged” the Pope as the antichrist and the devil’s apostle. As long as there is God's law, there is judgment. The law is eternal. So is judgment.
The Bible tells in John 7:24, "Do not judge according to appearance, but judge with righteous judgment.” In other words, if we are going to judge, we are to do it righteously using God's Word. We are to do it with love mercy and not malice. We should always remember the golden rule, "And just as you want men to do to you, you also do to them likewise" (Luke 6:31).