It's God's desire and will to have people to be able to judge, to discern, and to clarify matters or any given situation. In the Old Testament, there are two books titled Judges. Both books recorded people who were annointed by God to bring peace, help and salvation to the Israelites. These annointed ones are called Judges. Their task is to (to use modern cliche) 'uphold the law and protect the innocents'. It is through judgement that God's people able to enjoy justice and genuine love.
These 3 are just a few, out of many others, example found in the Bible:
Peter and John urged their accusers to judge.
1 Cor 6:4-6
Paul ridicule those Corinthians who doesn't know how to judge.
1 Cor 6:2-4
Paul encourages the Corinthians to judge because eventually the saint will judge together with God in eternity.
There are many many other verses from the New Testament that Christians are urged to judge. Sometimes NT writters dont use the word 'judge', they use 'discern' which don't differ much from the word 'judge'.
But aren't there verses that encourage Christians not to be judgemental?
Yes and no.
Yes, because these verses exist and explicitly command a 'non-judgemental' behaviour. No , because whenever such exhortation found, the immediate context gave a rather different meaning to our understanding of 'judgement'. Such non-encaouragable judgement usually are those related to the kind that accompanied by condemnation which is fatalistic and unloving. NT writters encourage Christians not to be judgemental, basically, means that we are not to judge unwisely, unprogressively, and unlovingly. We should not judge destructively. Whenever we judge, make sure we do it constructively. Our judgement should be purposed for building up instead of tearing down people.
Judgement itself is not condemnation. Judgement is discernment according to God's revelation for us, with faith in the atoning death of Jesus Christ for the world and the illumination of the Holy Spirit through the Bible. This is a Christian judgement.
It is the task and obligation for Christians to judge wisely, lovingly, constructively and (also) self-reflectively. Many jumped into the judgement seat hastilly without realizing that it is actually the accused seat. The famous exhortation is found in Matthew 7.
"Do not judge, or you too will be judged. For in the same way you judge others, you will be judged, and with the measure you use, it will be measured to you.
"Why do you look at the speck of sawdust in your brother's eye and pay no attention to the plank in your own eye? How can you say to your brother, 'Let me take the speck out of your eye,' when all the time there is a plank in your own eye? You hypocrite, first take the plank out of your own eye, and then you will see clearly to remove the speck from your brother's eye.
"Do not give dogs what is sacred; do not throw your pearls to pigs. If you do, they may trample them under their feet, and then turn and tear you to pieces.The first verse seems to nail it hard on those people like me who encourages judgemental behaviour but if one read only that verse alone, it is not surprising that one will reach that kind of 'out-of-context' conclusion and missed the whole point.
Note the last 3 sentences. Jesus meant it more like a reminder to his audience to judge properly (proper in the sense of wisely, lovingly, constructively, self-reflectively) rather emphasizing a decree that forbid any kind of judgement. "...first take the plank out of your own eye, and then you will see clearly to remove the speck from your brother's eye..." This verse make Jesus sounds like he is asking us to judge ourselves first before judging others. In fact, i believe that was what Jesus said. Self-reflective judgement seems to be a necessity if ever any judgement is to be constructive. In the way Jesus used "...and then..." shows that proper judgement is to be practiced so that it leads to building up people (to use Reformed language: sanctifying saints).
The last sentence obviously presume a judgemental mentality if ever that command is to be carried out. If one cannot judge properly (that is lovingly, wisely, constructively and self-reflectively), one would not be able to appropriate things. In order for one to practice appropriation (do not give to dogs and pigs what is precious/ give to caesar what belongs to caesar and to God what belongs to God), judgement is inevitable. In fact, judgment (or discernment or 'screening' or whatever you call it) is a must to live in this world that has been marred by so much falsehood, traps, and liars around. If this temporal world demands us to use our given judgemental instinct to survive and to service, how much more do we need to use it for the great kingdom of God.
The day is coming when the world is going to stand before a jury made up of Christians. If someday you are going to rule on the world's fate, wouldn't it be a good idea to practice on some of these smaller cases? Why, we're even going to judge angels! So why not these everyday affairs? - 1 Cor 6:2-3, The Message