The most common verse that gets taken out of context is Luke 6:37. What did Jesus mean by judge not and you will not be judged? It is about a judgmental attitude or being the final judge. People are called to judge sinful actions and wrong doctrine but not as the final judge. In John 7:24, Jesus said, "Judge not according to appearance but judge righteous judgment." In short, you are not to judge unrighteous judgment but righteous judgment. The kind of judgment that is forbidden is that when you judge wrongly. You are only permitted to judge righteously.
In further context, Matthew 7:1-2 is not the whole context either. Do you read the rest of the Bible or do you just cherry pick? Read Matthew 7:3-5 and you will realize that the instruction of judgment is that first you must judge myself before others. It says, "And why beholdest thou the mote that is in thy brother's eye but considerest not the beam that is in thine own eye? Or wilt thou say to thy brother, Let me pull out the mote out of thine eye; and behold a beam is in thine own eye? Thou hypocrite, first cast out the beam out of thine own eye and then thou shalt see clearly to cast out the mote out of thy brother's eye."