Similar Liturgical Practices Do Not Create Unity

The fact that two churches are going through the same liturgical actions does not mean there is unity. What someone thinks they are doing matters greatly. When a Roman Catholic celebrates the Mass they and the priest are doing something very different from what a Presbyterian pastor and his congregation are doing even though there is bread, wine, prayer, etc. Therefore unity cannot be built solely around doing the same liturgical actions.We must believe we are doing the same things and be doing them for the same reasons. When one group says,

The Council of Trent summarizes the Catholic faith by declaring: "Because Christ our Redeemer said that it was truly his body that he was offering under the species of bread, it has always been the conviction of the Church of God, and this holy Council now declares again, that by the consecration of the bread and wine there takes place a change of the whole substance of the bread into the substance of the body of Christ our Lord and of the whole substance of the wine into the substance of his blood. This change the holy Catholic Church has fittingly and properly called transubstantiation. (Roman Catholic Catechism, 1376)

And

The Eucharist is thus a sacrifice because it re-presents (makes present) the sacrifice of the cross, because it is its memorial and because it applies its fruit:

"[Christ], our Lord and God, was once and for all to offer himself to God the Father by his death on the altar of the cross, to accomplish there an everlasting redemption. But because his priesthood was not to end with his death, at the Last Supper "on the night when he was betrayed," [he wanted] to leave to his beloved spouse the Church a visible sacrifice (as the nature of man demands) by which the bloody sacrifice which he was to accomplish once for all on the cross would be re-presented, its memory perpetuated until the end of the world, and its salutary power be applied to the forgiveness of the sins we daily commit." [Quote from the Council of Trent] [RCC, 1366]

The sacrifice of Christ and the sacrifice of the Eucharist are one single sacrifice: "The victim is one and the same: the same now offers through the ministry of priests, who then offered himself on the cross; only the manner of offering is different." "In this divine sacrifice which is celebrated in the Mass, the same Christ who offered himself once in a bloody manner on the altar of the cross is contained and is offered in an unbloody manner."[Another quote from the Council of Trent, RCC 1367]

The Eucharist is also the sacrifice of the Church. the Church which is the Body of Christ participates in the offering of her Head. With him, she herself is offered whole and entire. She unites herself to his intercession with the Father for all men. In the Eucharist the sacrifice of Christ becomes also the sacrifice of the members of his Body. the lives of the faithful, their praise, sufferings, prayer, and work, are united with those of Christ and with his total offering, and so acquire a new value. Christ's sacrifice present on the altar makes it possible for all generations of Christians to be united with his offering. [RCC, 1368]

And the other groups says:

Do then the bread and wine become the very body and blood of Christ?

A: Not at all: but as the water in baptism is not changed into the blood of Christ, neither is the washing away of sin itself, being only the sign and confirmation thereof appointed of God; so the bread in the Lord's supper is not changed into the very body of Christ; though agreeably to the nature and properties of sacraments, it is called the body of Christ Jesus.

Why then does Christ call the bread "his body", and the cup "his blood", or "the new covenant in his blood"; and Paul the "communion of body and blood of Christ"?

A: Christ speaks thus, not without great reason, namely, not only thereby to teach us, that as bread and wine support this temporal life, so his crucified body and shed blood are the true meat and drink, whereby our souls are fed to eternal life;  but more especially by these visible signs and pledges to assure us, that we are as really partakers of his true body and blood by the operation of the Holy Spirit as we receive by the mouths of our bodies these holy signs in remembrance of him;  and that all his sufferings and obedience are as certainly ours, as if we had in our own persons suffered and made satisfaction for our sins to God.

What difference is there between the Lord's supper and the popish mass?

A: The Lord's supper testifies to us, that we have a full pardon of all sin by the only sacrifice of Jesus Christ, which he himself has once accomplished on the cross; and, that we by the Holy Spirit are grafted into Christ,  who, according to his human nature is now not on earth, but in heaven, at the right hand of God his Father,  and will there be worshipped by us.  But the mass teaches, that the living and dead have not the pardon of sins through the sufferings of Christ, unless Christ is also daily offered for them by the priests; and further, that Christ is bodily under the form of bread and wine, and therefore is to be worshipped in them; so that the mass, at bottom, is nothing else than a denial of the one sacrifice and sufferings of Jesus Christ, and an accursed idolatry. [Heidelberg Catechism Questions 78-80]

And

In this sacrament, Christ is not offered up to His Father; nor any real sacrifice made at all, for remission of sins of the quick or dead; but only a commemoration of that one offering up of Himself, by Himself, upon the cross, once for all: and a spiritual oblation of all possible praise unto God, for the same: so that the popish sacrifice of the mass (as they call it) is most abominably injurious to Christ's one, only sacrifice, the alone propitiation for all the sins of His elect. [Westminster Confession of Faith, 23:3]

The outward elements in this sacrament, duly set apart to the uses ordained by Christ, have such relation to Him crucified, as that, truly, yet sacramentally only, they are sometimes called by the name of the things they represent, to wit, the body and blood of Christ; albeit, in substance and nature, they still remain truly and only bread and wine, as they were before.[Westminster Confession of Faith, 23:5]

That doctrine which maintains a change of the substance of bread and wine, into the substance of Christ's body and blood (commonly called transubstantiation) by consecration of a priest, or by any other way, is repugnant, not to Scripture alone, but even to common sense, and reason; overthrows the nature of the sacrament, and has been, and is, the cause of manifold superstitions; yes, of gross idolatries.[Westminster Confession of Faith, 23:6]

...There is not unity in any meaningful sense. Two churches having a minister, bread, wine, prayers, and the Word during the Lord's Supper does not mean there is unity. We must also believe we are doing the same thing.