What is the basis for the Eucharist not being shared with non-believers? If the Eucharist is Christ (whether physical and/or spiritual), then that is Christ with us, and ‘supping’ with us. “Us” in this case is often restricted to believers or church members, yet Jesus regularly had supper with sinners that were not yet believers or followers - and was criticized for that.
Since the elements are Jesus Himself, why wouldn’t we want non-believers to be filled with Him? Wouldn’t this “make” a person filled with God?