Why does the OPC require that someone be a member of a "Bible believing church" to take communion? I don't think Christ stipulated this and thought the Lord's table was for all believers, whether they were church members or not. Where does the Bible say you must be a church member to receive communion?
You asked the question at the end of your post, "Where does the Bible say you must be a church member to receive communion?" This is a good question. There isn't any one verse that expressly stipulates that one must be a member of a local church to partake of communion. However, there are many things that the Scriptures teach as a whole that cannot be proved from simply one verse or passage. The Trinity, for example, is one of these teachings. Our approach to who may and may not partake of the Lord's Supper must follow the same pattern. There may not be any one passage that stipulates that church membership is a prerequisite for partaking of the Lord's supper, but the whole of the Bible's teaching on the church and the Lord's supper certainly seems to suggest that this is the case.
For example, we know from the pages of Scripture that there were local churches in the New Testament. In fact, of the 110 occurrences of the word "church" in the NT, over 90 of them refer to a local body of believers that are identifiable. That is why Paul will speak of the church in Galatia, Ephesus, Corinth etc. Therefore, when the Apostle rebuked the Corinthians for their abuse of the Lord's Supper, he was addressing a particular (gathered) body of Christ with an identifiable membership. Also, notice that in Acts 2:42 we are told that those who were saved in Acts 2:41 continued steadfastly in the apostles' doctrine, and fellowship, in the breaking of bread, and in the prayers. The breaking of bread there has often been understood to be a celebration of the Lord's supper, but notice, it happened after they were added by baptism to the church in Jerusalem. Furthermore, besides Christ's institution of the Supper with the apostles (on whose teaching the church is built, along with the prophets, Eph. 2:20) there is no instance of the sacrament being granted to those who are outside the visible church. This should give us great pause in regularly distributing the elements to those who refuse to join with a church of Jesus Christ.
Also it's helpful to notice that Q&A 168 of the Westminster Larger Catechism, asks "What is the Lord's supper?" The answer, among many other things, is that in the celebration of communion believers "testify and renew their thankfulness, and engagement to God, and their mutual love and fellowship each with other, as members of the same mystical body" (emphasis mine). In other words, believers not only express their communion with Christ in the Lord's Supper, but their communion with one another as the body of Christ. Such communion as the body of Christ is expressed in participation in the visible church. In other words, everything in the Scriptures seem to suggest that the Lord's Supper is celebrated within the confines of the visible church by those who are committed to the visible church.
With that said, there may be some circumstances in which someone is not a formal member of a local church and could take communion (perhaps they've left their church because of its unfaithfulness, or they are between churches; perhaps they go to a church in which there is not formal membership, but an informal membership process). This, however, is to be the exception, not the rule. In such exceptional circumstances, the decision whether to admit someone to the Lord's table should be left to the wisdom of the session of the local church.
In summary, then, though there is not one text that says, "you must be a member of a local congregation to take communion," there is every indication in the Scriptures that this was the practice of the churches of the New Testament, and the very meaning of the Lord's supper as a profession of communion with one another underscores this point.
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