“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. (Matthew 7:1-5 NKJV)
But now I have written to you not to keep company with anyone named a brother, who is sexually immoral, or covetous, or an idolater, or a reviler, or a drunkard, or an extortioner— not even to eat with such a person. For what have I to do with judging those also who are outside? Do you not judge those who are inside? But those who are outside God judges. Therefore “put away from yourselves the evil person.” (I Corinthians 5:11-13 NKJV)
Let's go ahead and examine these two passages. The first person talking here was Jesus. He was saying that we basically need to be minding our own sin. We have no right to judge another persons sin. We need to first examine ourselves and our own life. He ends the text with "and then you will see clearly to remove the speck from your brother's eye". Now, that kind of throws a wrench in this whole thing doesn't it? He is implying that we can help another person remove sin from their life. Notice though that he said "brother". When you see this in scripture, it is talking about another believer. In summary, we are to first examine our own lives and remain repentant of our own sin. If we do that, we can gently and lovingly lead our brothers and sisters in removing sin from their life as well. Notice though that he says nothing about non-believers.
This brings us to our next scripture where the apostle Paul is speaking. He is teaching to not associate with people who are part of the church and who call themselves brothers or sisters that are continuing in unrepentant sin proudly as if they never knew Christ. He says in that respect, we can judge (but still love and pray for) those in the church. He also confirms what Jesus was talking about in that we are not to judge those who are not in Christ. That is God's job.
And if anyone hears My words and does not believe, I do not judge him; for I did not come to judge the world but to save the world. He who rejects Me, and does not receive My words, has that which judges him— the word that I have spoken will judge him in the last day. (John 12:47, 48 NKJV)
Once again, Jesus is speaking here. He is talking about the time that is for judging and the standard by which people will be judged. Those who have accepted Christ won't have to worry about judgement because we have out on the righteousness of God through the blood of Christ. But those who have not accepted Him as He said Himself have their judge. They will be judged by His righteous Word in the last day. His righteousness makes even the best person on earth look filthy. That's the standard you will have to measure up against if you chose to take present your own works before God.
Judgment isn't for today. Today is not the last day. The bible says that today is the day of salvation. For Christians, your only job today is to love people and pray for them. Serve them and show them mercy just as your Father has shown you mercy. I didn't repent because I was afraid of judgement. I repented and followed Jesus because He loved me when I didn't deserve love. He offered me something I could never earn. Show that unconditional love to someone else today. It doesn't matter how they have sinned. You have too. Today isn't the day of judgement and you aren't burdened with the responsibility to judge. For those of you who don't know this merciful God who came down and became a humble man and took your punishment upon Himself, I pray that you find Him. He is merciful and longs to be with you now and forever. Yes. There is judgement coming someday. No. We can't judge other people and shouldn't try. Yes. God loves you and He would love to have one less person to judge according to His Word and one more to judge according to the perfect blood of Jesus.