There are some exceptions. The most notable is for members or the Orthodox Churches, who may receive Holy Communion, as well as Penance and Anointing of the Sick, when they request them spontaneously. Outside of exceptional circumstances, clearly defined in canon law, Protestants are not to receive Holy Communion, and in no case are the non-baptized to be allowed to receive the Holy Eucharist.
This disposition is not a lack of friendliness with non-Catholics, but simply the consequence of what it means to receive Holy Communion. That act means the person who receives it assents to everything the Church teaches. Non-Catholics do not.
Holy Communion is also a sign of unity. Most Catholic churches have missalettes in the pews, and most missalettes reprint the USCCB's "Guidelines for the Reception of Holy Communion." in part, they state:
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 holy Communion.
Sample extract from Catholic Answers to Catholic Questions (page 87).
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