This may the the passage of Scripture that is the most often quoted out of its context. 

Matthew 7:1 Judge not, that ye be not judged.

Its context:

Matthew 7:1-5 Judge not, that ye be not judged. For with what judgment ye judge, ye shall be judged: and with what measure ye mete, it shall be measured to you again. 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 how 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 shalt thou see clearly to cast out the mote out of thy brother's eye.

It's possible to judge types of actions and still leave the judgment of persons to God. Saying that a certain act is a sin is not hateful and it's not the same as judging others. We may say that something's an abomination without judging any person.

Note that the passage above talks about a beam in your own eye.  That beam is simply this: not being able to discern the Body of Christ.  If you cannot see the anointing that is on your brother or sister, you have no place trying to help them with their spiritual struggles.  Even if you see yourself as superior to the unsaved, you have no place trying to help them with their spiritual struggles either.  If you are saved, it is not because you are superior to anyone.  It is because of the mercy of God.

If we call someone a liar, that's taking the role of judge.   We do well, on the other hand, if we encourage everyone to refrain from lying. On the other hand it would be wrong to teach everyone that lying, cheating, and stealing are OK.  That's true of lying or any other sin.   
 
Our purpose in writing or speaking about these types of things is to bring people to Jesus so they can be healed and turn from sin. The Scripture speaks of those who love darkness more than they love light.  When we speak the truth in love, that is light.  When are honest and caring enough to tell the truth in love, there are some who will reject that light.  They may be offended by the light, even if they are born-again Christians.  When they are offended, they may accuse and slander those who spoke the truth.  If you are persecuted because you have done and spoken righteousness, then you should be very happy.  You have suffered with Christ.  They didn't reject you.  They rejected Christ, Himself. 

The following Scriptures should help to clear things up: 

John 7:24 Judge not according to the appearance, but judge righteous judgment.

6:1-5 Dare any of you, having a matter against another, go to law before the unjust, and not before the saints? Do ye not know that the saints shall judge the world? and if the world shall be judged by you, are ye unworthy to judge the smallest matters? Know ye not that we shall judge angels? how much more things that pertain to this life? If then ye have judgments of things pertaining to this life, set them to judge who are least esteemed in the church. I speak to your shame. Is it so, that there is not a wise man among you? no, not one that shall be able to judge between his brethren?

1 Corinthians 2:15 But he that is spiritual judgeth all things, yet he himself is judged of no man.

1 Corinthians 10:15 I speak as to wise men; judge ye what I say.

1 Corinthians 11:13-14 Judge in yourselves: is it comely that a woman pray to God uncovered? Doth not even nature itself teach you, that, if a man have long hair, it is a shame to him?

1 Corinthians 14:24 But if all prophesy, and there come in one that believeth not, or one unlearned, he is convinced of all, he is judged of all:

Luke 6:37 Judge not, and ye shall not be judged: condemn not, and ye shall not be condemned: forgive, and ye shall be forgiven:

1 Corinthians 4:3-5 But with me it is a very small thing that I should be judged of you, or of man's judgment: yea, I judge not mine own self. For I know nothing by myself; yet am I not hereby justified: but he that judgeth me is the Lord. Therefore judge nothing before the time, until the Lord come, who both will bring to light the hidden things of darkness, and will make manifest the counsels of the hearts: and then shall every man have praise of God.

Here are some forms and rituals that are not to be a means of judging:  
Colossians 2:16-17 Let no man therefore judge you in meat, or in drink, or in respect of an holyday, or of the new moon, or of the sabbath days: Which are a shadow of things to come; but the body is of Christ.

Here is Jesus speaking:  
John 12:47-48 And if any man hear my words, and believe not, I judge him not: for I came not to judge the world, but to save the world. He that rejecteth me, and receiveth not my words, hath one that judgeth him: the word that I have spoken, the same shall judge him in the last day.

John 5:22 For the Father judgeth no man, but hath committed all judgment to the Son: That all men should honour the Son, even as they honour the Father. He that honoureth not the Son honoureth not the Father which hath sent him. Verily, verily, I say to you, He that heareth my word, and believeth on him that sent me, hath everlasting life, and shall not come into condemnation; but is passed from death to life.