Why Non-Orthodox are excluded from the Sacrament of Holy Communion
In the light of Church history, the question might better be asked, "Why does anyone allow for open Communion". The fact is, from the very beginning, the Eucharist was offered only to baptized and chrismated believers. The 2nd century writing known as The Didache instructs believers to "let no one eat or drink from the Eucharist except those who are baptized in the Lord's name". So restrictive were the Eucharistic meetings of Christians in the first centuries that rumors arose among the pagans that they were actually involved in human sacrifice and cannibalism.
Even reformed churches practiced closed communion. Only baptized believers who had undergone examination by the leaders of the churches were admitted to the Lord's Supper. In times past, communion tokens were used to gain admission to the sacrament as, for example in the Church of Scotland and also in Methodist churches.
The Orthodox Church does not consider it sufficient to express belief in Jesus in order to be admitted to the sacrament. Many heretics believe in Jesus. Arius the 4th century heretic, believed in Jesus. Jehovah's Witnesses, Mormons and 7th Day Adventists believe in Jesus as do Hindus. But none of these or other groups believe in the One Lord Jesus Christ known and proclaimed by the One, Holy Catholic and Apostolic Church.
In the historic understanding of the Church, Communion has always been understood as the goal, the climax and expression of our unity in Christ. Today there are over 25,000 denominations worldwide and among them are many different views of Jesus.
The Orthodox practice closed communion, not for triumphalistic reasons, but for very important theological reasons. In doing so they follow the practice of the ancient Church; a practice that was retained by the Reformers. "Open communion" was a relatively recent innovation and an exception to the practice of the Church beginning in the New Testament period.
In our pluralistic American culture, we object to anything that excludes individuals. We have been taught that all faiths are relative in their claims. One denomination is as good to another to the average American; the Orthodox Church appears to just one more "denomination". However the Orthodox Church pre-dates denominations, and the practice of the Orthodox Church pre-dates the practices of later Christian denominations by at least 1500 tears.