The Lord's Supper is more than merely a memorial to Christ's sacrifice. In many churches it is called "communion" because the Body of Christ on earth is His church. It is the unity we enjoy in Christ that makes the Church what it is.

Could you enjoy such unity with someone who believes, for example, that Mary is a co-redeemer and intermediary between God and Man? Or with a person who believes that Christ died "spiritually" but not physically? Could you share the bread and the cup with someone who believes that theose elements actually become the literal body and blood of Christ?

We are called as members of one body. Two cannot walk together unless they are agreed. That is why there are "organized churches." Now there are plenty of churches and denominations other than my own where I can enjoy the worship of God and the fellowship of my brethren in Christ, but with whom I could not fully participate as a matter of conscience informed by Scripture. Some things are simply too important to set aside. The sacraments being one of them; biblical worship being another (despite room for differences), church polity, etc. That is why joining with like-minded believers offers a chance to fully participate with them and experience the fullest possible unity in Christ.