The Catholic Church does not permit its faithful to receive Holy Communion outside the Catholic Church in non-Catholic communities, for example: a Protestant denomination. Hence, while a Protestant denomination may extend Communion hospitality to Catholics, it does not mean that Catholics are permitted to accept such hospitality.
As well, those who are not Catholic cannot recieve the Eucharist in the Catholic Church. For Catholics, the Eucharist is a visible sign of unity; to receive Communion in a community to which one does not belong is improper. If one does not accept all that the Catholic Church believes and teaches and worships, one cannot make a visible sign of unity with it.
The Eucharist is the result of unity, not the means by which unity is achieved. While many non-Catholics see this as a sign that the Catholic Church excludes non-Catholics from the Eucharist, the opposite is true. Because a non-Catholic individual has chosen not to embrace all that Catholic Christianity holds, the non-Catholic individual makes it impossible for a Catholic priest to offer him or her communion. It is not so much a matter of Catholicism excluding the non-Catholic as it is the non-Catholic making it impossible for the Catholic to offer the Eucharist.
Sometimes people argue, “But I believe everything the Catholic Church teaches.” If this is indeed the case, then the question is not one of Eucharistic hospitality but, rather:
“Then if you believe everything the Catholic Church teaches, why haven’t you become a Catholic?”
Jesus doesn’t want us to have only some of what He offers us. Jesus wants us to have all of Him. Jesus doesn’t want us to come to Him for bits and pieces of Him. Through His Church Jesus gives us the means to encounter Him fully, in all He came to give us.
“I came that they may have life, and have it abundantly.”John 10:10
Jesus wants the best for each one of us. This is why He founded the Church – as the main means by which we encounter Him.
“And I tell you, you are Peter, and on this rock I will build my church, and the powers of death shall not prevail against it. I will give you the keys of the kingdom of heaven, and whatever you bind on earth shall be bound in heaven, and whatever you loose on earth shall be loosed in heaven.”Matthew 16:18-19
Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, teaching them to observe all that I have commanded you; and lo, I am with you always, to the close of the age.”Matthew 28:19-20