The New Testament basis for Christian Separation is the fact that Christ's people are one body in Christ, not only when praying but when playing, working or anything else. The key passages describing exclusive cooperation among Christ's people in all kinds of activity are the "body" passages, such as 1st Corinthians 12 and Romans 12. I see no reason to suppose that these refer only to certain areas of activity. The natural assumption is that they apply to all areas.
"A little yeast affects the whole batch."
1st Corinthians 5:6 (warning that admitting wrongdoers will hinder getting the job done).
"Avoid being diversely yoked with distrusters. For what partnership have propriety and lawlessness? Or what fellowship has light with darkness? What symphony has Christ with Belial? Or what share has a truster with a distruster?"
2nd Corinthians 6:14-15. (I see no evidence that he spoke only of marriage.)
"You are ... a separate nation, God's own people."
1st Epistle of Peter 2:9. (Not just a priesthood within a nation. This illustrates how intrinsic the Separation principle was to early Christianity. Sadly it was eroded and then swept away as Christianiodity degenerated into Statism.)
The following objections have all actually been raised. Many of them appeal to the Bible, but the replies show that they misconstrue it. Some are so fatuous that it is difficult to know how to reply, but I have tried to identify serious underlying points wherever possible, and I think it valuable to record them if only to illustrate their weakness.
I must even find arguments for it at a venture, and ransack my own imagination for such phantoms as I can find to fight with.
Jeremy Bentham, Defence of Usury
"The apostles' appeal to Christ's people to separate from the world only applies to certain areas of activity. Obviously it applies to things like prayer groups. The only other possible area is marriage. (1st Corinthians 7.15 suggests that mixed marriages could be problematical.) There is nothing in the New Testament to suggest that any other kind of relationship would be affected."
There is no reason why prayer groups should be more exclusive than business partnerships or other groups. There is no basis for the limitation to a few areas, or rule to judge where the boundary is, except the traditional division into spiritual and ordinary areas. This tradition is part of the modern notion that friendship with God is a merely personal matter, a leisure activity, and therefore unimportant, so that we can safely allow ourselves an exclusiveness in such matters that would be harmful if applied in more important matters like business, education and politics.
"Christ sent his people into the world (John 17.18). So frequent and regular cooperation with wrongdoers in a wide range of activities is good."
Your first statement is true but your second does not follow from it. Christ sends his people into the world to cultivate its resources. This involves setting wrongdoers an example and calling them to repent, but there is no suggestion, here or anywhere else in the New Testament, to join in their culture and organisations, and the New Testament as a whole is against such an interpretation.
"Jesus welcomed everyone. So in forming relationships we should make no distinction between God's people and outsiders."
Both of your statements are ambiguous. It depends what you mean by welcome, and it depends what kinds of relationship you mean.
Jesus was willing to talk to everyone, and everyone was invited to follow him. But those who refused to follow him were kept at arm's length. When Jesus was resting or praying, he took only his disciples with him.
Furthermore, even some of what might seem like integrationism on Jesus' part is illusory. At that point in the history of God's relations with humanity, all Jews were, in a sense, God's people. In that sense, as far as is known, Jesus ate only with God's people. And he deliberately did not preach in Gentile lands, since his task was as a prophet among God's people rather than an evangelist beyond them. (Evangelism to the gentiles has of course since then become legitimate. The point is merely that, in the context of his mission, Jesus was a separatist.)
"God approved of Naaman's continuing to work for the King of Syria, even though it involved participation in overt idolatry (2nd Kings 5.18). This illustrates how relaxed God is about his people working with outsiders."
In the conditions of the time, Naaman's position was not just a job but a deeply entrenched obligation, more like (and possibly based on) family ties than a modern contract of employment. I do not advocate breaking up such ties, only being careful about entering into them.
"God's people are not perfect, so they have no right to separate themselves from wrongdoers."
This objection is sheer nonsense, as the conclusion does not follow from the premise. It seems to be based on some confused combination of the following two objections.
(1) "God's people have been forgiven by God, but in itself this does not change their conduct and for all practical purposes they are still wrongdoers like anyone else. So God's people should treat each other the same way they should treat anyone else."
Your first statement is false. The Bible tells us that God's people are very different from wrongdoers and must be treated differently (1st John 2.4). This text, and the many others teaching that God's people not only should but also do live godly lives, are often ignored, while those that describe God's forgiveness towards his people when they lapse in that godliness are wrongly taken to imply that one who has been forgiven could live a life consisting of nothing but lapses.
(2) "God does not make people his friends because they are better than others, but enables them to be better. So they should cooperate fully with wrongdoers."
Your first statement is true but your second does not follow from it. The fact that we were the same as they does not imply that we should act as if we still are.
"Many who ignore organised evangelism will listen to the same message from someone with whom they are already friendly. So God's people should integrate into the surrounding society to help outsiders to hear the gospel."
The premise clearly has some truth in it. If the gospel were something like a personal hygiene regime, the conclusion would be valid. The problem is that the gospel, and the life to which the hearer is invited, are incompatible with integration. To preach the gospel while setting an example of integration is impossible, for the example undermines the message.
The idea that every welldoer has a duty to spread the gospel (sometimes called personal evangelism) is unbiblical, along with the integration that naturally goes with it. The New Testament assumes, on the contrary, that evangelism is a gift given to some, and while mentioning many duties of Christians in general never mentions evangelism among them.
Incidentally, even if we could ignore such basic principles, the contribution of personal evangelism would be impossible to assess. False Christianity has prevailed among Evangelicals throughout modern times. So, even assuming we had a method for assessing such contributions, we could only assess personal evangelism's contribution to the preaching of false Christianity. How could we assess its contribution to the preaching of real Christianity? Real Christianity would need to have flourished for a generation. I am confident that being able to point to the example of an at least embryonic Christian alternative to English society would more than compensate for the lack of opportunities for personal evangelism.
Back to Humanity's Unchanging Task (3).