Church discipline can be difficult, and I’m certainly not going to pretend to have all of the answers, but if we look at 1 Corinthians 5, Paul clearly seems to indicate that there is a way that we should treat those who call themselves Christians and those who make no such claim.
1Co 5:11 But now I have written unto you not to keep company, if any man that is called a brother be a fornicator, or covetous, or an idolater, or a railer, or a drunkard, or an extortioner; with such an one no not to eat.
1Co 5:12 For what have I to do to judge them also that are without? do not ye judge them that are within?
1Co 5:13 But them that are without God judgeth. Therefore put away from among yourselves that wicked person.
I think that the best way to approach this topic is to consider what it means to be a Christian. We agree to certain things as Christians. As much as identifying as an accountant comes with the expectation of certain pieces of information and expertise, being a Christian means that we are identified with certain things.
One thing that we ought to agree on is the authority of Scripture. I know that people disagree on certain interpretations of Scripture, but I think we all ought to agree on the fact that the Bible is a guide to life. If we agree that the Bible ought to influence how we live our lives, then we have a common ground to identify violations of that agreement.
For people who are not Christians and do not agree to the Bible as an important piece of God’s revelation, it is not possible to hold them to the same standard because they don’t know the standard. We can still identify sinful behavior, but we should not be surprised when people who are not Christians don’t live in the way that God wants us to live.
However, Christians, or at least people who identify as Christians, understand what God expects of us, and as a result, it seems to be the case that one a fellow Christian falls into something that he or she should know is wrong, then we have the responsibility to help him or her correct that relationship with God.