"Judge not, that you be not judged." (Matthew 7:1 -- NKJV)
"Do not speak evil against one another, brothers. The one who speaks against a brother or judges his brother, speaks evil against the Law and judges the Law. But if you judge the Law, you are not a doer of the Law, but a judge. There is only one Lawgiver and Judge, He who is able to save and to destroy. But who are you to judge your neighbor?" (James 4:11-12 -- ESV, slightly modified)
"I wrote to you in my letter not to associate with sexually immoral people -- not at all meaning the sexually immoral of this world, or the greedy and swindlers, or idolaters, since then you would need to go out of the world. But now I am writing to you not to associate with anyone who bears the name of brother if he is guilty of sexual immorality or greed, or is an idolater, reviler, drunkard, or swindler -- not even to eat with such a one. For what have I to do with judging outsiders? Is it not those inside the Church whom you are to judge? God judges those outside. Purge the evil person from among you." (1 Corinthians 5:9-13)
"Or do you not know that the saints will judge the world? And if the world is to be judged by you, are you incompetent to try trivial cases? Do you not know that we are to judge angels? How much more, then, matters pertaining to this life!" (1 Corinthians 6:2-3)
"Who are you to pass judgment on the servant of another? It is before his own master that he stands or falls. And he will be upheld, for the Lord is able to make him stand." (Romans 14:4)
"Stop judging by mere appearances, and make a right judgment" (John 7:24)
It should be clear, I hope, that the question of whether or not Christians are to be judges of the character, actions, or eternal destiny of others -- whether inside or outside the Church -- is filled with tension.
The reason I list these passages (and there are, of course, more) is due to the recent spat on various social media platforms about the Supreme Court, DOMA, and the possibility of legalizing homosexual marriage. I've seen accusations, counter-accusations, counter-counter-accusations, and so on. "You're being judgmental!" And, as seems to be true in the Christian world online these days, there is the inevitable descent to name-calling, ad hominems, red herrings, and general snarky "well-I'm-right-and-if-you-don't-agree-with-me..." on either side of the issue. Not only is there no agreement on the issue, or on the validity of judgment over the issue, there is not an ounce of civility to be had. Part of this, I think, is that civil dialogue has been replaced, culturally, by a sort of weak-spined relativistic pluralism, especially evident amongst evangelicals of a younger sort.
What I'm encouraging, and hope to find time to write on in the near future, is a return ad fontes, to the source, to the Scriptures and the historical witness of the Church, as the starting-point for understanding what is going on and how we, the Church, might address it properly. The texts above stand as a initial salvo. Exegetical work needs to be done.
A few notes, though, from my own point of view, that might be important in setting out terms for debate. (Note, please, that I'm treating this in my normal fashion as an intra-Church debate. Theoretically, we share the same presuppositions, but don't necessarily do so with those "outside". I'm not interested, at this point, of debating with those outside of the Church community. Not that such debate isn't important or necessary, but I don't think the Church is quite ready for that...yet).
1) Christendom is over. We don't have the political clout of yesteryear. No emperors (or presidents or supreme courts) are out to protect our interests.
2) The "Religious Right" and "Moral Majority" are over. See #1. The moral bankruptcy of both major political parties in the USA is well known. We religious folk have been played as suckers by those in power. And we will continue to be suckers as long as we suck at the teet of those in power. If you want to fight homosexuality as a political issue, that is fine, but don't pretend that Republicanism or conservativism are just the political expression of Christianity. They aren't and they never were. Neither, though, is Democratism or liberalism. All of them are indebted to an Enlightenment rejection of the authority of the Church over any but the most private matters (if you don't believe me, read Locke's "Letter[s] Concerning Toleration" -- thanks to Caleb for the correction). Politically, the name of the game is the fact-value division: any attempt to overcome it is, frankly, treasonous. And it is treated as such by both parties.
3) Don't assume people "outside" care about your opinion, no matter how Biblically based it is. We've lost our moral voice (the Catholic sex-scandal, Ted Haggard, etc.), which will take generations of hard, humble work to reestablish. When we say something is Biblical, people automatically see hypocrisy. We cannot blame that on them, either. Judgment starts in the House of God, I've read somewhere.
4) Don't assume people "inside" care about your opinion, no matter how Biblically based it is. See #3. Same reasons apply.
5) Civility is important. Learn it. Being arrogant, brusque, or hasty does not equal a good argument.
6) Proper authority is important. Here is one I think we especially need to attend to. What constitutes "proper" authority in God's Church? Just because you are a college professor of Bible does not make you an authority. Authority is derived from the holy Spirit through a life of holiness, compassion, mercy, justice, compassion, long-suffering, humility, holiness, and compassion.
That should get us started.