St Paul writes about this and its seems that this was a big problem in the ancient Church.
In the words of St Paul, its a fallacy and falsehood to believe that Christians cannot judge. Judging people inside the Church and outside the Church are two different things. St Paul says that we are to judge those people inside of the Church but not to judge outsiders. (1 Corinthians 5:12).
St Paul says, "Do you not know that we are to judge angels? How much more, then, matters pertaining to this life!" (1 Corinthians 6:3.
"For what have I to do with judging outsiders? Is it not those inside the church whom you are to judge? God judges those outside. “Purge the evil person from among you.” " (1 Corinthians 5:12-13)
So basically, as St Paul told us, we are to judge the people who are in the Church, discerning as to whether they are a good influence to the Christian community.
Making a judgment of any kind, we are never to think that we are better than these people, never never. St Paul still says, "This is a trustworthy saying, and everyone should accept it: "Christ Jesus came into the world to save sinners"--and I am the worst of them all."
( 1 Timothy 1:15 ESV)
When it comes to Christs words, "Judge not", St John the Chrysostom says:
HOMILY XXIII: MATT. VII. 1.
"Judge not, that ye be not judged."
WHAT then? Ought we not to blame them that sin? Because Paul also saith this selfsame thing: or rather, there too it is Christ, speaking by Paul, and saying,(1) "Why dost thou judge thy brother? And thou, why dost thou set at nought thy brother?" and, "Who art thou that judgest another man's servant?"(2) And again, "Therefore judge nothing before the time, until the Lord Come."(3)
How then doth He say elsewhere, "Reprove, rebuke, exhort,"(4) and, "Them that sin rebuke before all?"(5) And Christ too to Peter, "Go and tell him his fault between thee and him alone," and if he neglect to hear, add to thyself another also; and if not even so doth he yield, declare it to the church likewise?"(6) And how hath He set over us so many to reprove; and not only to reprove, but also to punish? For him that hearkens to none of these, He hath commanded to be "as a heathen man and a publican."(7) And how gave He them the keys also? since if they are not to judge, they will be without authority in any matter, and in vain have they received the power to bind and to loose.
And besides, if this were to obtain, all would be lost alike, whether in churches, or in states,(8.) or in houses. For except the master judge the servant, and the mistress the maid, and the father the son, and friends one another, there will be an increase of all wickedness. And why say I, friends? unless we judge our enemies, we shall never be able to put an end to our enmity, but all things will be turned upside down.
What then can the saying be? Let us carefully attend, lest the medicines of salvation, and the laws of peace, be accounted by any man laws of overthrow and confusion. First of all, then, even by what follows, He hath pointed out to them that have understanding the excellency of this law, saying, "Why beholdest thou the mote that is in thy brother's eye, but considerest not the beam that is in thine own eye?
But if to many of the less attentive, it seem yet rather obscure, I will endeavor to explain it from the beginning. In this place, then, as it seems at least to me, He doth not simply command us not to judge any of men's sins, neither doth He simply forbid the doing of such a thing, but to them that are full of innumerable ills, and are trampling upon other men for trifles. And I think that certain Jews too are here hinted at, for that while they were bitter accusing their neighbors for small faults, and such as came to nothing, they were themselves insensibly committing deadly(10) sins. Herewith towards the end also He was upbraiding them, when He said, "Ye bind heavy burdens, and grievous to be borne, but ye will not move them with your finger,"(11) and, "ye pay tithe of mint and anise, and have omitted the weightier matters of the law, judgment, mercy, and faith."(12)
Well then, I think that these are comprehended in His invective; that He is checking them beforehand as to those things, wherein they were hereafter to accuse His disciples. For although His disciples had been guilty of no such sin, yet in them were supposed to be offenses; as, for instance, not keeping the sabbath, eating with unwashen hands, sitting at meat with publicans; of which He saith also in another place, "Ye which strain at the gnat, and swallow the camel."(13) But yet it is also a general law that He is laying down on these matters.
And the Corinthians(14) too Paul did not absolutely command not to judge, but not to judge their own superiors, and upon grounds that are not acknowledged; not absolutely to refrain from correcting them that sin. Neither indeed was He then rebuking all without distinction, but disciples doing so to their teachers were the object of His reproof; and they who, being guilty of innumerable sins, bring an evil report upon the guiltless.
This then is the sort of thing which Christ also in this place intimated; not intimated merely, but guarded15) it too with a great terror, and the punishment from which no prayers can deliver.