Greek word is “fellowship”
The Lord’s Supper is a shared fellowship of believers, done in rememberance of Him until He comes again.
The word is κοινωνία. The meaning is more than "fellowship" but "communion, association, partnership." But communion with what? Not of "believers" but of the "blood of Christ" and of the "body of Christ." By the sharing of the Eucharist we become one with the body and blood of Christ.
“But communion with what? Not of “believers”
Yes. A fellowship together, remembering His sacrifice.
STRONGS:
Definition: (lit: partnership) (a) contributory help, participation, (b) sharing in, communion, (c) spiritual fellowship, a fellowship in the spirit.
HELPS WORD-studies: 2842 koinōnía (a feminine noun) – properly, what is shared in common as the basis of fellowship (partnership, community).
34.5 κοινωνίαa, ας f: an association involving close mutual relations and involvement—‘close association, fellowship.
Louw, J. P., & Nida, E. A. (1996). Greek-English lexicon of the New Testament: based on semantic domains (electronic ed. of the 2nd edition., Vol. 1, p. 445). New York: United Bible Societies.
When read in context with the other passages involving the Last Supper, we see we are told to "do this in remembrance of Me."
The word for remembrance is ἀνάμνησις conveying the meaning of : Cognate: 364 anámnēsis (from 363 /anamimnḗskō, "bring to mind") – properly, deliberate recollection, done to better appreciate the effects (intended results) of what happened; active, self-prompted recollection especially as a memorial.
29.11 ἀνάμνησις, εως f: (derivative of ἀναμιμνῄσκω ‘to cause to remember,’ 29.10) the means for causing someone to remember—‘means of remembering, reminder.’ Louw, J. P., & Nida, E. A. (1996). Greek-English lexicon of the New Testament: based on semantic domains (electronic ed. of the 2nd edition., Vol. 1, p. 347). New York: United Bible Societies.
Just as the blood was always poured out and never consumed in the OT sacrifices, so is the blood poured out and never consumed in the NT.
The only way we can participate with Christ is to believe in His Words...that is, to believe in Him and follow Him.
When we have the Lord's Supper we are signifying we are His. It recalls the sacrifice of His body and blood on the Cross for our behalf.
If the Roman Catholic wants to maintain we can only appropriate Christ through eating and drinking of His flesh and blood, then no unbeliever will ever be able to come to Christ in this manner.
Only believers are to participate in the Lord's Supper. If you don't believe you don't participate, hence you cannot come to salvation through the Roman Catholic perspective.
However, Christianity, which follows the NT, shows we come to Christ through belief/faith in Him as He told us.