The issue of church membership is not dealt with in the Scriptures for one simple reason: In the days when the Scriptures were written, there were not multiple churches in one city. There was just one local church per city, and any believer living in that city was automatically a member of that local church under the authority of the elders of that city. Hence, there was no need for church membership.
In light of what has happened since then, church membership has become an important issue. The believer is committed to a specific local body if he is willing to be supportive of the body both financially and in the use of his spiritual gifts, but also be in subjection to the leadership of that local body.
Obviously church discipline cannot be imposed upon nonmembers, which is why church membership is vital. Anytime there is a moral issue that would bring disrepute upon the local church, church discipline needs to be imposed. Those who are members are held to a higher standard. If a member goes into sin, church discipline should be imposed, especially if it is a moral issue.
The couple you mentioned who are living together outside of marriage but are not members of the congregation, cannot be disciplined by your church at this point. But their immoral lifestyle should definitely be dealt with.
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Arnold Answers is a bi-weekly Q & A with founder and director of Ariel Ministries, Dr. Arnold G. Fruchtenbaum.