Judge not, that you be not judged. For with the judgement you pronounce you will be judged, and with the measure you use it will be measured to you. Why do you see the speck that is in your brother's eye, but do not notice the log that is in your own eye? Or how can you say to your brother, "Let me take the speck out of your eye" when there is the log in your own eye? You hypocrite, first take the log out of your own eye, and then you will see clearly to take the speck out of your brother's eye.
"Don't judge" is probably the most quoted verse in the bible. We use it to excuse anything. We see it as the ultimate defense to any criticism. Reading this verse in context, we see that it is not about never making a judgement about anything or anybody[1] but about hypocritical judgement - judging others while letting yourself off the hook.
We do this all the time. We are quick to see other people's faults but ignore our own. We are outraged that someone else has committed a particular sin but we justify our own. We criticise others and expect them to change but bristle at any criticism we receive or any suggestion something needs to change in our own life.
This isn't new - Calvin observed the same thing:
We see how all flatter themselves, and every man passes a severe censure on others. This vice is attended by some strange enjoyment: for there is hardly any person who is not tickled with the desire of inquiring into other people’s faults...This depraved eagerness for biting, censuring, and slandering, is restrained by Christ, when he says, Judge not. It is not necessary that believers should become blind, and perceive nothing, but only that they should refrain from an undue eagerness to judge
Jesus instructions are not about never confronting sin, or about needing to be blameless before doing it. It is about being more concerned about our own sin than the sin of somebody else. It is about looking at ourselves more than we look at others. Life in the Christian community should include rebuke, confession and repentance but that doesn't work with people who are eager to criticise. It is supposed to take place between people who are aware of their own sin and so approach each other humbly.
[1] 1 - that would be impossible 2 - Jesus tells us to be discerning (Matt7:6) - which involves making a judgement 3 - Jesus instructs us how to address sin in others lives (Matt 18:15-17) - which also involved making a judgement