expel the immoral brother

Just today I read over 1 Corinthians 5. It describes a sexually immoral person in the church whom Paul asks that they expel from the church. Towards the end, it makes an excellent distinction between people in the church and outside - we are only to disassociate with those inside the church who are stubbornly immoral (in this case, proud of it). People on the outside we should still work with. So often I think this distinction has been overlooked in the Kingdom and has resulted in both condemnation of unbelievers, a holier-than-thou effect, and unholy tolerance of lukewarm Christians in the church who are living in sin.

I think the passage describes it well: 1 Corinthians 5:9-13 "I wrote to you in my letter not to associate with sexually immoral people - not at all meaning the people of this world who are immoral, or the greedy and swindlers, or idolaters. In that case you would have to leave this world. But now I am writing to you that you must not associate with anyone who claims to be a brother or sister but is sexually immoral or greedy, an idolater or slanderer, a drunkard or swindler. Do not even eat with such people. What business is it of mine to judge those outside the church? Are you not to judge those inside? God will judge those outside. 'Expel the wicked person from among you.'"

Essentially the principle towards not-yet-Christians is this: if they don't believe the law of God, if they don't believe that behaving according to his will will bring them closer, if they don't want to be closer to God, if they don't even believe he exists in any way, what right do we have to ask them to behave as if they do? It's like saying 'You shouldn't eat meat!' to someone who's decidedly not a vegetarian. You don't yell at somebody for something they've decided, fully consciously, to do! 

On the other hand, for those who have decided to follow God, you have a pretty good case. Following God includes some pretty basic and undisputed things, including not persisting in huge sin stuff and letting others hold you accountable to it. If someone you know claims to be a Christian yet is, for instance, living with his/her girl/boyfriend unmarried, you have every right to yell at them (well, to confront them. Use love in every and all situations, but you get what I mean). God didn't let our sin slide, he killed his son brutally to show us that he's not satisfied with imperfection and un-awesomeness. So don't you let sin slide either. 
Three caveats to this:
1) If someone struggles with a sin, repeatedly doing it but struggling to walk in the light and take steps to eradicate the sin, don't call them out. They're working on it, chill out. If you're their close friend and involved in the process, well yes, let them know when you discover that they've done it again, it helps. Also, if they're only half-trying - 'oh, I sinned again, darn, I guess I'll have to try harder next time' - let them know that won't cut it either. If current methods of squashing sin aren't working, you need to keep trying different things. If more openess, more sacrifice, more life routine change is neccessary, so be it. This is not an area where we have liberty to take it half-on.
2) There will be gray cases of sin. For instance, some may think it's a sin to drink alcohol. People will disagree on how far into their life you should go to befriend unbelievers. For instance, can you go to a bar, or a place where there are strippers? This must be dealt with by 'food sacrificed to idols'. The principle appears in 1 Corinthians 8 (whole chapter) in the context of food sacrificed to idols, so that's what I call the principle. Basically, different people have different limits depending on what they believe and what they can handle. "All things are permissible, but not all things are beneficial" If you know that you will fall into sin by going somewhere, don't go. If you know you can handle it, go ahead. If by going you know that you will embolden younger, weaker, or confused believers to sin, don't go. And obviously, think of the unbelievers too. If by going they will think that you are compromising on your faith, don't. Otherwise, go ahead. 
3) There are some issues (extremely few) that are debatable. (Romans 14 deals with this). In this case "Accept him whose faith is weak, without passing judgement on disputable matters" So basically again, if someone thinks drinking is a sin (and you don't), don't drink around them. Maybe don't drink at all just for their sake. Stuff that is kind of gray (like Rom 14 mentions whether we should keep Sunday separate) don't worry about. Fight over Jesus being God and other stuff. 

So, end principle: don't yell at unbelievers, but please yell at those who claim to be Christians yet practice pretty blatant sin.