The guidelines for receiving Communion, which are issued by the U.S. bishops and published in many missalettes, explain, "We welcome our fellow Christians to this celebration of the Eucharist as our brothers and sisters. We pray that our common baptism and the action of the Holy Spirit in this Eucharist will draw us closer to one another and begin to dispel the sad divisions which separate us. We pray that these will lessen and finally disappear, in keeping with Christ’s prayer for us ‘that they may all be one’ (John 17:21).
"Because Catholics believe that the celebration of the Eucharist is a sign of the reality of the oneness of faith, life, and worship, members of those churches with whom we are not yet fully united are ordinarily not admitted to Communion. Eucharistic sharing in exceptional circumstances by other Christians requires permission according to the directives of the diocesan bishop and the provisions of canon law. . . . "
Scripture is clear that partaking of the Eucharist is among the highest signs of Christian unity: “Because there is one bread, we who are many are one body, for we all partake of the one bread” (1 Cor. 10:17). For this reason, it is normally impossible for non-Catholic Christians to receive Holy Communion, for to do so would be to proclaim a unity to exist that, regrettably, does not.
Another reason that many non-Catholics may not ordinarily receive Communion is for their own protection, since many reject the doctrine of the Real Presence of Christ in the Eucharist. Scripture warns that it is very dangerous for one not believing in the Real Presence to receive Communion: “For any one who eats and drinks without discerning the body eats and drinks judgment upon himself. That is why many of you are weak and ill, and some have died” (1 Cor. 11:29–30).
Catechism of the Catholic Church:
1400 Ecclesial communities derived from the Reformation and separated from the Catholic Church, "have not preserved the proper reality of the Eucharistic mystery in its fullness, especially because of the absence of the sacrament of Holy Orders."239 It is for this reason that, for the Catholic Church, Eucharistic intercommunion with these communities is not possible. However these ecclesial communities, "when they commemorate the Lord’s death and resurrection in the Holy Supper . . . profess that it signifies life in communion with Christ and await his coming in glory."240
1401 When, in the Ordinary’s judgment, a grave necessity arises, Catholic ministers may give the sacraments of Eucharist, Penance, and Anointing of the Sick to other Christians not in full communion with the Catholic Church, who ask for them of their own will, provided they give evidence of holding the Catholic faith regarding these sacraments and possess the required dispositions.241