Biblical Separation

Can two walk together, except they be agreed? (Amos 3:3 KJV)

Separation is natural, and sometimes, necessary.

Examples of natural separation

1. Truth from lies;
2. Light from darkness;
3. Sick from healthy (especially in hospitals).

Christians also need to separate, based on scriptures, to God and holiness.

Separation from sin
Abstain from all appearance of evil. (1 Thessalonians 5:22 KJV)

Separation from the world
Do not be unequally yoked with unbelievers. For what partnership has righteousness with lawlessness? Or what fellowship has light with darkness? What accord has Christ with Belial? Or what portion does a believer share with an unbeliever? What agreement has the temple of God with idols? For we are the temple of the living God; as God said, "I will make my dwelling among them and walk among them, and I will be their God, and they shall be my people. Therefore go out from their midst, and be separate from them, says the Lord, and touch no unclean thing; then I will welcome you, and I will be a father to you, and you shall be sons and daughters to me, says the Lord Almighty." (2 Corinthians 6:14-18 ESV)
Ye adulterers and adulteresses, know ye not that the friendship of the world is enmity with God? whosoever therefore will be a friend of the world is the enemy of God. (James 4:4 KJV)

Separation from immoral brethren
If your brother sins against you, go and tell him his fault, between you and him alone. If he listens to you, you have gained your brother. But if he does not listen, take one or two others along with you, that every charge may be established by the evidence of two or three witnesses. If he refuses to listen to them, tell it to the church. And if he refuses to listen even to the church, let him be to you as a Gentile and a tax collector. (Matthew 18:15-17 ESV)
I wrote to you in a letter not to associate with sexually immoral people. I did not mean the immoral people of this world or the greedy and swindlers or idolaters; otherwise you would have to leave the world. But now I am writing you not to associate with anyone who claims to be a believer who is sexually immoral or greedy, an idolater or verbally abusive, a drunkard or a swindler. Do not even eat with such a person. (1 Corinthians 5:9-11 HCSB)

Separation from brethren who believe in false doctrines

Reject a divisive person after a first and second warning, knowing that such a person is perverted and sins, being self-condemned. (Titus 3:10-11 HCSB)
Anyone who does not remain in Christ’s teaching but goes beyond it, does not have God. The one who remains in that teaching, this one has both the Father and the Son. If anyone comes to you and does not bring this teaching, do not receive him into your home, and don't say, "Welcome," to him; for the one who says, "Welcome," to him shares in his evil works. (2 John 1:9-11 HCSB)
I appeal to you, brothers, to watch out for those who cause divisions and create obstacles contrary to the doctrine that you have been taught; avoid them. (Romans 16:17 ESV)

Effects of non-separation

1. Separation from God
But your iniquities have separated between you and your God, and your sins have hid his face from you, that he will not hear. (Isaiah 59:2 KJV)
2. Infection
Do not be deceived: "Bad company ruins good morals." (1 Corinthians 15:33 ESV)
Leaven - false doctrine
A little leaven leavens the whole lump. (Galatians 5:9 ESV)
Leaven - immorality
Your boasting is not good. Do you not know that a little leaven leavens the whole lump? (1 Corinthians 5:6 ESV)

3. Destruction
Separate yourselves from among this congregation, that I may consume them in a moment. (Numbers 16:21 KJV)
But I have a few things against you: you have some there who hold the teaching of Balaam, who taught Balak to put a stumbling block before the sons of Israel, so that they might eat food sacrificed to idols and practice sexual immorality. So also you have some who hold the teaching of the Nicolaitans. Therefore repent. If not, I will come to you soon and war against them with the sword of my mouth. (Revelation 2:14-16 ESV)
Then I heard another voice from heaven saying, "Come out of her, my people, lest you take part in her sins, lest you share in her plagues; for her sins are heaped high as heaven, and God has remembered her iniquities. (Revelation 18:4-5 ESV)