Towards the end Christopher Yuan talked about how parents upon finding out that an older child is gay should not kick them out of the house. (Click here to watch the video at the place where Chris starts.)
Aside from the issue of homosexuality, this brings up a point about the role that believing families play in the reconciliation of unrepentant sinners to God.
In 1 Corinthians 5, Paul wrote:
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 ESV)
This is a command for the church. People in the church are to be judged by the church. People not in the church are judged by God. The hoped-for result is given in verse 5:
...you are to deliver this man to Satan for the destruction of the flesh, so that his spirit may be saved in the day of the Lord. (1 Corinthians 5:5 ESV)
The meaning may not be clear to some people. It doesn't mean to kill the person and let God deal with them. It means that the person should be removed from the church in the hope that they will eventually be reconciled. In a sense, this is what God did with the human race in Genesis 3. He separated is from him so that we would not be judged right away, but have the opportunity to be reconciled as we come to understand God's promise of salvation in the Messiah.
While individuals are called to faith, families composed of faithful individuals are extensions of the church. Presbyterians baptize infants of believers as being part of the covenant of faith that is bore out in the local family. Baptists like myself don't do that. But we still recognize that families of believers are called to carry the testimony of faith outside the church by demonstrating the covenant of faith.
At this point, one may be tempted to say that a family of faith may be called as part of the local church to put out a family member who has fallen into unrepentant sin, but we need to look at what a "family of faith" really is. We can identify a mother and father who are faithful believers in Christ and who have brought their children up in the local church. Unless you believe in baptismal regeneration and are paedobaptistic, those children are not Christians until they can genuinely profess Christ. That's a best-case scenario. So what about if only one parent is a believer? What about if neither parent is a believer and one or more the children become Christians? You don't have a clean-cut case for the family being an immediate extension of the church.
Rather, what you have is what Paul wrote about only a couple of chapters later:
To the rest I say (I, not the Lord) that if any brother has a wife who is an unbeliever, and she consents to live with him, he should not divorce her. If any woman has a husband who is an unbeliever, and he consents to live with her, she should not divorce him. For the unbelieving husband is made holy because of his wife, and the unbelieving wife is made holy because of her husband. Otherwise your children would be unclean, but as it is, they are holy. But if the unbelieving partner separates, let it be so. In such cases the brother or sister is not enslaved. God has called you to peace. For how do you know, wife, whether you will save your husband? Or how do you know, husband, whether you will save your wife? (1 Corinthians 7:12-16 ESV)
The believer in this case is an extension of the ministry of the gospel of the local church to their families. I suggest that it is the same if you have most of a family who is saved and one who goes astray.
Therefore, where a person may be put out of the church because of unrepentant sin (which is really an outworking of unbelief) the family members who remain faithful must leverage their familial relationship to minister the gospel to that person. Don't put them out of the family. Continue to love them. Listen to them. Be safe for them to confide in. And when it comes time don't be afraid to share the truth in love, not as ones who are righteous, but who are repentant sinners bought with a price, even the blood of Christ.