"Do not judge, and you will not be judged; and do not condemn, and you will not be condemned; pardon, and you will be pardoned."
When Jesus says we should not judge others, He doesn't mean we shouldn't evaluate another person's actions, their beliefs or the things that they teach. If this were the case, then we would accept whatever is presented to us, whether it is right or wrong. The judgment Christ is talking about is the judgement that condemns; that is self-righteous. This judgment looks down on another person and assumes we know the motives of their heart. In our extreme attempt as a culture to be tolerant we miss the necessity to be discerning. And discernment is something we're called to be. "If your brother sins, go and show him his fault in private; if he listens to you, you have won your brother. But if he does not listen to you, take one or two more with you, so that by the mouth of two or three witnesses every fact may be confirmed. If he refuses to listen to them, tell it to the church; and if he refuses to listen even to the church, let him be to you as a Gentile and a tax collector." Matthew 18:15-17
("Gentile" and "tax collector" in this case would describe an unbeliever. Someone who is unrepentant.) The Apostle Paul instructed the church to discern also. "I wrote you in my letter not to associate with immoral people; I did not at all mean with the immoral people of this world, or with the covetous and swindlers, or with idolaters, for then you would have to go out of the world. But actually, I wrote to you not to associate with any so-called brother if he is an immoral person, or covetous, or an idolater, or a reviler, or a drunkard, or a swindler—not even to eat with such a one. For what have I to do with judging outsiders? Do you not judge those who are within the church? But those who are outside, God judges. Remove the wicked man from among yourselves." (1 Corinthians 5:9-13) Clearly Christ's words in Luke 6:37 do not mean we should disregard the sin in other people's lives.