No. This is very dangerous. St. Paul warns that because people do not recognize the Body and Blood of the Lord many of them are sick and dying. Unless a person fully recognizes the Body and Blood of the Lord, and their own sinfulness is confessed and forgiven they are asking for trouble. The Church makes provisions for those who are in danger of dying and don't have time to go through the classes and whatnot to speak to a priest. In danger of death, one might speak to a priest and be allowed confession and the Eucharist if one is baptised and truly believes in the Eucharist. Failing that, one must go through classes and confession (the Sacrament of Penance) or be baptised first. Even Catholics are risking a lot when they are taking Holy Communion unworthily.
If you mean: "why shouldn't a non-Catholic receive the Eucharist in a Catholic Church, then answer is because a non-Catholic is, by choice, separated from The Catholic Church and does not accept or believe (or fully understand) the teachings of The Catholic Church as it pertains to the Eucharist. If a non-Catholic doesaccept the teachings of The Catholic Church, then he/she should convert to Catholicism and become a full member of The Church. Receipt of the Eucharist in the Catholic Church implies communion with The Catholic Church. Why do that if true & full "communion" does not exist? To do so is disingenuous at best. As Christians, we all need to respect each others teachings and not cavalierly dismiss/violate them. Even Catholics may not receive The Eucharist if they have committed a "mortal" sin (serious/deadly sin). They must first confess, and genuinely repent, their sin(s) via the Sacrament of Reconciliation/Penance. And, all Catholics can know which sins are considered "mortal" by consulting the Catechism of the Catholic Church. Receiving The Eucharist in The Catholic Church is a very serious matter -- we are receiving The Body, Blood, Soul & Divinity of Our Lord Jesus Christ. Because of that, all Catholics must be in "a state of Grace" in order to receive lawfully and respectfully. That means respectful not merely (or even primarily) to Church law but rather respectfully and lovingly toward Our Lord Jesus Christ.
Anabaptist
In the church.
in a convoluted sense yes you do, its not the normal Eucharist though.
Eucharist is a form of Initiation to the church to receive God's Communion.
You must receive the Eucharist properly because it is a solemn and ancient religious ritual, and if you do not do it properly you would be showing disrespect to that tradition.
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Catholics must receive the Eucharist at least once per year during the Easter season.
Eucharist
Who is going to know and hold you accountable if you don't confess your sins before taking the Eucharist?
When you receive the Eucharist, you remember that is is the Body and Blood of Christ, and Christ gave himself up for all of us.
The Eucharist gives one the "food of eternal life." The Eucharist also allows us to receive the Lord and shows us that we are committed to Him. The Eucharist also is the initiation into Christ's body and blood which was shed for us. Therefore Eucharist is a sacrament of Initiation.
Catholics and others are welcome to attend an Orthodox service, but they are not permitted to receive the Eucharist, as this is reserved for members of the Orthodox Faith alone.