First of all, it is not possible to have sound Biblical judgment without being born again and having the Holy Spirit in one's heart.  (The apostle Paul says “Examine yourselves, whether ye be in the faith; prove your own selves. Know ye not your own selves, how that Jesus Christ is in you, except ye be reprobates?”  [2 Cor 13:5].  The presence of the Holy Spirit must be known, it is not a 'pretend' or make-believe presence.)
   Today's fundamentalists hold to lots of correct doctrine and rules and consider themselves spiritually discerning, since they can see some unbiblical things taught by mainstream churches.  The problem is that they themselves have fallen into a trap.  They teach a false, 'repentance-free - pretend-Holy Spirit' gospel that cannot result in the new birth and hence the gift of the Holy Spirit.  So while they have enough spiritual discernment to convince themselves that all is good, they too fall short and miss the boat.  So close and yet so far.
   So, before turning my attention to others, I should ask myself:  Am I a reprobate?  Do I have the Inner Witness, the Holy Spirit?  Do I know? 
    Romans 8:16:  "The Spirit itself beareth witness with our spirit, that we are the children of God"  1 John 4:13:  "Hereby know we that we dwell in him, and he in us, because he hath given us of his Spirit"  1 John 3:24:  "And he that keepeth his commandments dwelleth in him, and he in him. And hereby we know that he abideth in us, by the Spirit which he hath given us."  1Jo 5:10:  “He that believeth on the Son of God hath the witness in himself:” Isaiah 32:17:  “And the work of righteousness shall be peace; and the effect of righteousness quietness and assurance for ever.”  Do I know?
   If I can't say yes, than while I might judge some things Biblically and escape one trap, I will fall into a more refined trap and miss the boat along with those I was judging. 
   Holy Spiritless judging turns a group into a cult with a bunch of rules and teachings.  And if it's very close to the truth it is all the more deadly.
    Also Truth does not reveal itself to a rebel. God taught me that He will not teach the man who is not willing to obey.  He will not satisfy the merely curious or the proud.  As humans we are sinners in rebellion against God.   In the Garden of Eden, man disobeyed God, rebelled against God.  The Bible says that  "rebellion is as the sin of witchcraft" (1 Samuel 15:23).  Unbelievers are called "the children of disobedience" (Ephesians 2:2; 5:6; Colossians 3:6).  
    The Bible speaks to born again Holy Spirit filled believers and says not to have fellowship with brethren who walk disorderly: 

   "Now we command you, brethren, in the name of our Lord Jesus Christ, that ye withdraw yourselves from every brother that walketh disorderly, and not after the tradition which he received of us."  (2 Thess 3:6)   “And if any man obey not our word by this epistle, note that man, and have no company with him, that he may be ashamed.  Yet count him not as an enemy, but admonish him as a brother."  (2 Thess 3:14-15)  The hope is that "God peradventure will give them repentance to the acknowledging of the truth" (2 Tim 2:25); and it also protects the individual from being tempted to fall into sin/error.

   So, God wants us to take a stand for the Truth, in the Truth.  “Watch ye, stand fast in the faith”  (1 Co 16:13)  and  “earnestly contend for the faith which was once delivered unto the saints”  (Jude 1:3).  

   But is it Biblical to judge?

   There are different types of 'judging' in the Bible:

1.  Judging hypocritically is forbidden (Matthew 7).
2.  Judging on the basis of personal preference in matters not commanded in the Bible is
     forbidden (Romans 14).
3.  We are also not to judge motives (1 Co 4:1-5).
4.  However the child of God has an obligation to judge everything by God's indwelling Holy Spirit and His

    The Bible says "without me ye can do nothing."  (John 15:5) and James 4:15:  "For that ye ought to say, If the Lord will, we shall live, and do this, or that."  The Word of the Lord came in power.  One can't be spiritually discerning without the Spirit.
    The Holy Spirit is called "the Spirit of Truth".  The Lord Jesus Christ said "I am the way, the truth...".  This means that the Lord Jesus is Himself the Truth and I can only know Truth if I am in Him, if His Holy Spirit is in me.  Then through the Holy Spirit's illumination of my understanding as I read the Bible He opens my eyes to 'untruth'; error, false teachers, spirits...: 
    "Beloved, believe not every spirit, but try the spirits whether they are of God: because many false prophets are gone out into the world."  (1 Jo 4:1)  So, we are to try the spirits.  (The word 'try' means to test, examine, or prove.)  How can I in my own strength with my old nature try spirits? 
    We are also to judge preaching "Let the prophets speak two or three, and let the other judge"  (1 Cor 14:29). ('prophets' means 'inspired speaker'.)   We are to judge sinning church members (1 Cor 5:3).  And we are to judge doctrine (1 Tim 1:3). 
    1 Cor 2:15 says "But he that is spiritual judgeth all things".  If I am not spiritual, if I don't have the Holy Spirit I am kidding myself if I think that I can judge - sure I might be extremely discerning, but I will simply fall into a more refined trap of the devil and perish with those whom I am judging.
    The Lord Jesus Christ commanded:  "Judge not according to the appearance, but judge righteous judgment" (John 7:24).  If I am not in Christ, abiding in Him, how could I possibly judge righteous judgment through my old nature ?
    The Apostle Paul writes: "And this I pray, that your love may abound yet more and more in knowledge and in all judgment; that ye may approve things that are excellent" (Phil 1:9-10). 
    Disputes between Christians should be judged by a tribunal of fellow Christians: "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" (1 Cor 6:1-4).

   The Corinthians are rebuked because they were careless in NOT judging:  "For I am jealous over you with godly jealousy: for I have espoused you to one husband, that I may present you as a chaste virgin to Christ. But I fear, lest by any means, as the serpent beguiled Eve through his subtilty, so your minds should be corrupted from the simplicity that is in Christ. For if he that cometh preacheth another Jesus, whom we have not preached, or if ye receive another spirit, which ye have not received, or another gospel, which ye have not accepted, ye might well bear with him"  (2 Cor 11:2-4).

   The Beareans were praised for testing everything by the scriptures:  “These were more noble than those in Thessalonica, in that they received the word with all readiness of mind, and searched the scriptures daily, whether those things were so”  (Acts 17:11).

   The Apostles spent lots of time warning about false doctrine and doctrines of devils.  Some examples:

• "Now the Spirit speaketh expressly, that in the latter times some shall depart from the faith, giving heed to seducing spirits, and doctrines of devils"  (1 Tim 4:1)

• "I marvel that ye are so soon removed from him that called you into the grace of Christ unto another gospel: Which is not another; but there be some that trouble you, and would pervert the gospel of Christ. But though we, or an angel from heaven, preach any other gospel unto you than that which we have preached unto you, let him be accursed. As we said before, so say I now again, If any man preach any other gospel unto you than that ye have received, let him be accursed." (Gal 1:6-8)

• "Brethren, be followers together of me, and mark them which walk so as ye have us for an ensample. (For many walk, of whom I have told you often, and now tell you even weeping, that they are the enemies of the cross of Christ" (Phil 3:17-18)

• "Beware lest any man spoil you through philosophy and vain deceit, after the tradition of men, after the rudiments of the world, and not after Christ."  (Col 2:8)

• "I charge thee therefore before God, and the Lord Jesus Christ, who shall judge the quick and the dead at his appearing and his kingdom; Preach the word; be instant in season, out of season; reprove, rebuke, exhort with all longsuffering and doctrine. For the time will come when they will not endure sound doctrine; but after their own lusts shall they heap to themselves teachers, having itching ears; And they shall turn away their ears from the truth, and shall be turned unto fables."  (2 Tim 4:1-4)

• All of 2 Peter 2 talks about false teachers.

   We are called to "reprove, rebuke, exhort with all longsuffering and doctrine"  (2 Tim 4:2).  This involves making Biblical judgments as the Holy Spirit illuminates me through His Word.

   Modern secular philosophy tells us not to judge, to love everybody, that nobody is right/wrong, that there are no absolutes; and this idea has made its way into the church. However, this is not Biblical.  What kind of love is it not to judge and not to tell someone who believes in a false gospel that it will take him to hell?

   How do we know that abortion is wrong?  That murder is wrong?  How do we know what is right and what is wrong?  We know because God says so.  Therefore, we are *judging* abortion, murder... on the basis of the Bible.

   It is clearly Biblical to judge; and it is a matter of wisdom and obedience to do so.
   It is only true born again Christians who can judge in this world (won’t we even judge angels? 1Co 6:3), by the Holy Spirit and the Word of God; as non-Christians don't have anything by which to judge and false believers have traditions, rules, doctrines (which can all be very good and Biblical) - but is nevertheless only the "letter" of the Bible, but not the Spirit.  2 Corinthians 3:6:  "Who also hath made us able ministers of the new testament; not of the letter, but of the spirit: for the letter killeth, but the spirit giveth life."  Today's fundamental churches reek of the stench of death.
    We shouldn't be "children, tossed to and fro, and carried about with every wind of doctrine, by the sleight of men, and cunning craftiness, whereby they lie in wait to deceive"  (Eph 4:14).

   As mentioned before, the Bible warns us that "evil men and seducers shall wax worse and worse, deceiving, and being deceived" (2 Tim 3:13).   So the Bible says "prove all things; hold fast that which is good" (1 Thess 5:21) and "believe not every spirit, but try the spirits" (1 John 4:1).  And this is only possible if one is born again and has a new nature and has the Inner Witness, the Holy Spirit and is abiding in Christ.