I respect WELS position on close(d) Communion, but don't fully understand the logic. In numerous posts you've stated that only God can look into a person's heart, that Christians of other denominations may have saving faith, and the like. Further, denominations other than WELS believe in the Real Presence of Christ in Communion. It only makes sense that people should be regularly communing in their own church. But why do you insist on complete doctrinal agreement on every point before you allow someone to commune? After all, at family reunions, not everyone gets along perfectly, but no one is denied the meal.
Perhaps it can be helpful if I build off your closing analogy. There is one family of believers, known only to God (1 Corinthians 3:16; Ephesians 1:23; 4:12; 2 Timothy 2:19). Because God alone knows who belongs to that church family, we call it the “invisible church.”
You and I live in the world of “visible churches”—one in which we can see who belongs to which church. Whether or not people realize it or acknowledge it, their membership in a church states that their faith lines up with that church’s teaching. When it comes to the practice of close communion, it is a matter of comparing the teachings of people’s churches with the Bible’s teachings.
“How many of the church’s teachings must line up with the Bible’s teachings for people to commune together?” you might ask. Nowhere does Scripture speak of anything that falls short of complete unity (John 8:31; 1 Thessalonians 5:21-22). In fact, the Bible speaks of the unity that is threatened by the spreading of any false doctrine (Galatians 5:9). The Bible calls upon Christians to be on the lookout for false doctrine, and to avoid it and those who persist in it (Romans 16:17).
One of the purposes of close communion is to ensure that, as far as humanly possible, the unity that is expressed by those receiving the Sacrament is genuine and not contrived (1 Corinthians 10:17). It would not be an accurate picture of unity if the people receiving the Lord’s Supper together represented churches that teach doctrines—of any kind—that are contrary to Scripture.
If there are visitors to our worship services who belong to churches whose teachings do not agree with biblical teaching, they are certainly welcome to stay and hear the word of God. The Lord directs us to share his gospel message with all people (Mark 16:15). On the other hand, there is no instruction in the Bible that authorizes an indiscriminate distribution of the Lord’s Supper. Visitors to our worship services who belong to churches whose teachings do not agree with biblical teaching may very well be part of the family of God by the saving faith that resides in their hearts. Again, God alone knows that. But if they received the sacrament in our churches, their actions would be saying they are united with our visible church family and its doctrines. Based on the different confessions of both churches, that would not be an accurate statement.
Today, the family of God is scattered among visible churches. The day will come, of course, when sin and all of its effects—including false doctrine—will no longer exist. Then, the family of God will enjoy perfect peace and unity. And then we will all be guests at the same meal (Revelation 19:9). I hope this response is helpful for you.