We had a school Mass very recently, and I'm pretty sure there were kids who went up to receive the Eucharist who weren't Catholic-Christian. Perhaps they did this out of ignorance or they did this out of spite believing that "any Christian" could go up and receive the body and blood of Christ at a Catholic Mass. So here's something you can share with non-Catholic Christians who believe they should be allowed to receive the Eucharist at a Catholic Mass, i.e. those who use the "Well Jesus gave it to everybody at the Last Supper anyway..." argument:
The fact is this: Yes, Jesus did give the bread and the wine to everybody at the Last Supper, but who was this "everybody"?
Christ's discourse on his body and blood as being "real food" and "real drink" (i.e. the Real Presence) found in John 6 took place approximately one year before the Last Supper. Jesus was preparing his disciples theologically (and to an extent psychologically) for this last communion in which they shared a mean, in which Jesus instituted the Sacrament of the Eucharist (Luke 22:19-20). Keep in mind that those who found Christ's words troubling and offensive walked away from Jesus (John 6:60-66). Only those who truly believed remained with Jesus (John 6:68-69), and only those who truly believed in the Real Presence were present at the Last Supper.
Anyone who doubted Christ's words found in John 6 were not there and did not share in the breaking of bread and the pouring of wine. This is why St. Paul wrote to the Corinthians (and thus all Christians) exhorting them to take proper care when participating in the breaking of bread and the pouring of wine (1 Corinthians 10:16; 1 Corinthians 11:23-29).
If you are not a Catholic, you cannot receive the Eucharist at a Catholic Mass. For more information about what Catholics believe about the Eucharist, go here: http://www.catholic.com/tracts/the-real-presence
What you can do, however, as a non-Catholic Christian at a Catholic Mass, is pray for a spiritual communion. This act of spiritual communion is an expression of desire to receive our Lord Jesus and allow him to be present sacramentally within us. Here is a prayer of spiritual communion found on the EWTN website (http://www.ewtn.com/devotionals/prayers/blsac4.htm):
My Jesus, I believe that You are present in the Most Holy Sacrament. I love You above all things, and I desire to receive You into my soul.
Since I cannot at this moment receive You sacramentally, come at least spiritually into my heart. I embrace You as if You were already there and unite myself wholly to You. Never permit me to be separated from You.
Happy Easter and the blessing of Christ be present with you on this Holy Thursday night.