Recently the question arose: may Catholics participate in the Lord’s Supper with Protestants? The answer is an unfortunate “No, we may not.” It is unfortunate because of the fact that Christians are not united, and it is for that reason necessary that we not participate in the Lord’s Supper with them.
The Catechism says:
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.” It is for this reason that Eucharistic intercommunion with these communities is not possible for the Catholic Church. 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.” [§1400]
Furthermore, this practice is forbidden by Canon Law:
Catholic ministers administer the sacraments licitly to Catholic members of the Christian faithful alone, who likewise receive them licitly from Catholic ministers alone. [CIC 844, §1]
The requirements of this canon depend for their necessity upon the necessity of the truth expressed by the Catechism.
Why is this important? Because Communion is an expression of the unity of the Church as Christ’s Body. An absolutely essential part of that unity is unity of belief. Why? Because the Lord Jesus Christ says that He is the way, the truth and the life (John 14:6). But if those who commune do not hold to what the Church teaches, then to that extent they are contradicting what Jesus said of Himself. An important thing to remember here is that the Church is not merely a human or earthly institution; as I said above, the Church is Christ’s Body. Consequently unity of belief is necessary just because He is truth Himself. To suggest that errors do not matter isn’t merely a question of being charitable or not. In the end, our very understanding of the nature of reality is at stake.
So we may not participate in Protestant ordinances like the Lord’s Supper precisely because we are not in full communion with them.