score:4
Richard's answer isn't really teaching for separation of church and state, but rather evidence against fighting it. It shows we are to obey the authorities, but it doesn't say the government cannot be a specific religion. Jesus never taught to keep it separated (that is recorded at least), so it cannot be taken as doctrine. At the same time, he also never preached that the unification is desired.
To have a government that has Christian values would, of course, be desirable (the Bible is considered to be the greatest book of morals ever written by a lot of non-Christians). However, Christianity is about choosing to have a relationship with Jesus. To have a government that forces everyone to be Christian could easily cause a lot of people to conform publicly, but resent Jesus privately. This is why I believe He never tried to make that unification.
Upvote:2
Interpretation of @Richard's previous answer aside I know of nothing in the New Testament that either endorses or condemns the concept of the separation of church and state. However, in Romans Paul instructs Christians to submit to the authorities that we are subject to.
Let every person be subject to the governing authorities. For there is no authority except from God, and those that exist have been instituted by God. 2 Therefore whoever resists the authorities resists what God has appointed, and those who resist will incur judgment. 3 For rulers are not a terror to good conduct, but to bad. Would you have no fear of the one who is in authority? Then do what is good, and you will receive his approval, 4 for he is God’s servant for your good. But if you do wrong, be afraid, for he does not bear the sword in vain. For he is the servant of God, an avenger who carries out God’s wrath on the wrongdoer. 5 Therefore one must be in subjection, not only to avoid God’s wrath but also for the sake of conscience. 6 For because of this you also pay taxes, for the authorities are ministers of God, attending to this very thing. 7 Pay to all what is owed to them: taxes to whom taxes are owed, revenue to whom revenue is owed, respect to whom respect is owed, honor to whom honor is owed.
The Holy Bible : English standard version. 2001 (Ro 13:1–7). Wheaton: Standard Bible Society.
I would conclude that the Bible takes the view that God sovereignly ordains whatever earthly authorities are in place, regardless of how we as humans conceive and structure them.