"And this food is called among us Εὐχαριστία [the Eucharist], of which no one is allowed to partake but the man who believes that the things which we teach are true, and who has been washed with the washing that is for the remission of sins, and unto regeneration, and who is so living as Christ has enjoined. For not as common bread and common drink do we receive these; but in like manner as Jesus Christ our Savior, having been made flesh by the Word of God, had both flesh and blood for our salvation, so likewise have we been taught that the food which is blessed by the prayer of His word, and from which our blood and flesh by transmutation are nourished, is the flesh and blood of that Jesus who was made flesh."
Having been reminded of this great quote of Justin Martyr (HT John Stephenson), we find again the great body of evidence that says that the only communion hospitality worth anything is that which proceeds from the common faith of those who discern Christ's body and blood, who live in repentant faith as the baptized, seeking to live the new life declared to them in that baptism by the Holy Spirit. Anything less than this unity of faith and common life flowing form the font only betrays the meal and the Lord who is host and food. It is not our supper or the Church's meal but Christ's table. It is His witness and words that tell us who is welcome and who is not -- less to exclude some than to prevent those not of the same faith from receiving to their harm the presence of Christ (meant sacramentally but which can surely also be judgment against the communicant when faith in these words is not present).
Interestingly, I have found it more common that people from other churches (non-sacramental) are more likely to tell me that this is indeed what they believe. To wit I must ask "Then why do you belong to a church that does not believe and teach thusly?" And therein lies the rub. Many pious Christians take the Word at its face value but belong to churches wherein that Word is denied. Now they do so for a variety of reasons but perhaps the hardest is to admit that the presence of Christ in the Supper is itself a doctrinal issue of the first part. So the challenge to them is not only why are in a church that does not confess and teach faithfully as you yourself acknowledge and why do you not condemn the error? Perhaps the typical answer is that we believe that the Lord's Supper is portable, that is, it is what I think it is and not what my present church home might believe. So what becomes operative here is the faith of the individual. They are less forthcoming at how it is possible for two people to be together at the rail and one receive the Body of Christ and the other merely bread. Lest we Lutherans think to highly of ourselves, this is the receptionist error that remains hidden among us as well. The presence of Christ is conditional upon the throat and faith of the believer or else Christ does not come. I do not understand how it is possible to hold onto such contradictory views but we as people are nothing if we are not inconsistent and fraught with contradiction. I am sure that I have my own inconsistencies as well. Which all the more points to the need for us to research what churches believe, confess, and teach and to be captive to the Word within the faithful confession.