Partaking of the sacrament is a witness to God that the remembrance of His Son will extend beyond the short time of that sacred ordinance. Part of this ordinance is a promise to remember Him always and a witness of individual willingness to take upon oneself the name of Jesus Christ and to keep His commandments. In partaking of the sacrament and making these commitments, Church members renew the covenant they made at baptism (see Mosiah 18:8–10; D&C 20:37).
But what about those who are not members of the Church? What covenants are they renewing? Should they be allowed to partake of the Sacrament? What do we tell them, and how can we be diplomatic about it? The What Do Mormons Believe blog addresses the issue very well. In the blogger's personal opinion, there is no harm in taking the Sacrament without being a member. No one is going to look at you like you’ve blasphemed their faith by partaking. But it is important to understand why we take the Sacrament: (1) It reminds us of our Lord and Savior, Jesus Christ and His great sacrifice on our behalf. (2) It serves as a renewal of the covenants we made at our baptism.
Essentially, it’s up to the individual. No one is under any obligation to take the Sacrament. If you feel more comfortable passing the tray along, that’s perfectly acceptable. If you’d like to take it, you’re welcome to do so, though it will mean far more to you after baptism. This weekly ordinance allows baptized and confirmed saints to maintain the constant companionship of the Holy Ghost, the greatest gift we can have in life.
This is the smart approach. Explain the ordinance, its meaning and applicability, then tell the investigator to make the final decision personally. Here's a classic example of how NOT to handle it. On April 12th, 2008, Mormon Matters posted this account of an investigator who had been given a chapel card, and showed up for church just as the sacrament service was beginning. When the bread tray came to him, he was unsure what to do, so he took a piece of the bread. Just then, an older missionary who was serving in a branch leadership role jumped up from his seat on the stand and commanded the man (in Spanish) to “Drop it!” which he did. Needless to say, the investigator never returned. To explain his actions, the missionary referred to 3 Ne. 18: 28-29:
28 And now behold, this is the commandment which I give unto you, that ye shall not suffer any one knowingly to partake of my flesh and blood unworthily
29 For whoso eateth and drinketh my flesh and blood unworthily eateth and drinketh damnation to his soul; therefore if ye know that a man is unworthy to eat and drink of my flesh and blood ye shall forbid him.
While this missionary was perhaps a bit overzealous in his application of these scriptures in this specific situation, there is clearly a scriptural prohibition to prevent someone taking the sacrament unworthily. In the August 1999 edition of The Ensign, Elder Dallin H. Oaks of the Quorum of the Twelve Apostles addressed this situation. Speaking about judgments, Elder Oaks said the following about partaking of the Sacrament:
...To be righteous, an intermediate judgment must be within our stewardship. We should not presume to exercise and act upon judgments that are outside our personal responsibilities. Some time ago I attended an adult Sunday School class in a small town in Utah. The subject was the sacrament, and the class was being taught by the bishop. During class discussion a member asked, “What if you see an unworthy person partaking of the sacrament? What do you do?” The bishop answered, “You do nothing. I may need to do something.”
Because the missionary was part of the branch leadership, it was within his stewardship to intervene. But it would have been much better had he waited until after the service was over before addressing the issue with the investigator.
Additional gems of wisdom about the Sacrament by various General Authorities are available HERE.