The Bible is clear in 1 Cor 5:12-13 and in other places in the Bible that Christians are supposed to judge matters within the church. Yet most professing Christians refuse to judge even the simplest things according to the Word of God for fear that they would be considered judgmental of brothers. But all throughout the Bible we see many Scriptures that tell us to reason, to think, to be on guard, to test and prove, to test all things, to reprove rebuke and exhort with all long suffering and doctrine, that the spiritual man judges all things (How? According to the Word of God), etc., etc.
Yet due to a common and popular misunderstanding of the context of Matt 7:1, often quoted in old English as, “Judge ye not lest ye be judged”, most Christians will not proclaim the clear judgments of Christ that we find in the Word of God, that which the Lord Jesus Christ has already judged to be good or bad. Further, these same people often get angry at Christians who do their duty and are willing to be persecuted, those who “earnestly contend for the faith” as we see in Jude 3.
We see clearly in Matthew Chapter 7, verse 1 through 5 that the context of Jesus’ warning here is not to judge hypocritically:
“Judge not, that you be not judged. For with what judgment you judge, you shall be judged: and with what measure you mete [apply], it shall be measured to you again. And why behold you the mote [twig] that is in your brother's eye, but consider not the beam that is in your own eye? Or how will you say to your brother, Let me pull out the mote [twig] out of your eye; and, behold, a beam is in your own eye? You hypocrite, first cast out the beam out of your own eye; and then shall you see clearly to cast out the mote [twig] out of your brother's eye.”
Many lift the above verses out of context to the exclusion of what the rest of the Scriptures teach in the area of judging sin, false doctrine, church-related issues, etc. They falsely justify judging nothing and refuse to proclaim the clear judgments of Christ as given in the Word of God. Certainly we need to clean out our own closets before attempting to help others clean out their closets. It is hypocritical to point out things in the lives of other people if we have not first repented of those very same things ourselves.
Also, Romans 2:1-6 is commonly misinterpreted as a command not to judge anything, when in fact that is not what is being said at all.
“Therefore you are inexcusable, O man, whosoever you are that judges: for wherein you judge another, you condemn yourself; for you that judge do the same things. But we are sure that the judgment of God is according to truth against them which commit such things. And do you think this, O man, that judges them which do such things, and do the same, that you shall escape the judgment of God? Or do you despise the riches of his goodness and forbearance and longsuffering; not knowing that the goodness of God leads you to repentance? But after your hardness and impenitent heart treasure up unto yourself wrath against the day of wrath and revelation of the righteous judgment of God; Who will render to every man according to his deeds:” Rom 2:1-6
These verses simply prohibit the act of passing condemning judgments such as sentencing a person as the judge in a court might do, or damming a person to hell, taking vengeance on them, etc. Romans 2:1-6 in no way contradicts the other Scriptures that, in so many words, clearly tell us to judge rightly according to the Word of God. There is a big difference between these false judgments and properly judging all things according to the Word of God, which is exactly what every Christian is supposed to do.
Additionally, 1 Corinthians 4:5 must not be misinterpreted as a license to avoid proper judgment:
"Therefore judge nothing before the time, until the Lord comes, 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."
This verse is referring to things like not presumptuously judging someone's eternal rewards. That is obviously not our job. That is for the Lord to judge. This verse is not negating our responsibility to test and prove someone's teachings and properly judge their doctrine to make sure that it is Scriptural.
Lastly, there are no conflicts in the Bible. We must therefore look for the harmony of all Scripture on a particular subject and then balance those verses together. If we elevate one verse to the exclusion of what the rest of the Bible teaches on the same subject, then we will misinterpret and misapply what the Bible is actually saying.