I’m going to comment on Lydia McGrew’s case for the real presence:
What I do believe is that Jesus is specially, spiritually present in the elements of Communion in the sense that they are spiritual food.
I don’t see the connection. In principle, something could be spiritual food without requiring the spiritual presence of Christ. For instance, God could simply assign a particular effect to a particular practice. Or you could have the sanctifying grace of the Holy Spirit.
God has so ordained that those of us who, as the Prayer Book says, have "duly received" Communion are objectively spiritually nourished thereby. In this sense Jesus objectively comes down to us in the bread and wine and gives himself, his life and spiritual strength, aka grace, to us when we rightly receive.
But the ascended Savior has a physical body. For him to “objectively come down” would be analogous to his appearing to the disciples after the Resurrection. Not hidden in a wafer, but as a visible, tangible man (e.g. Jn 21).
(And if we don't rightly receive, we could be in big trouble for profaning this Sacrament which has been rendered holy by God's intention that it should be a means of grace to us.)
Profanation doesn’t require objective presence. To take a comparison, desecrating a grave is a classic way of dishonoring your enemies (e.g. Amos 2:1; 2 Kgs 23:15-16). Yet that’s symbolic. You can’t actually harm your enemies at that point. They are gone. Although their mortal remains are physically present, your enemies aren’t really there. But the grave has emblematic significance. To desecrate a grave symbolically disrespects the dead.
When the consecrated Host is reserved on the altar, because the Host is that divinely ordained physical meeting point between our Lord Jesus Christ and ourselves, the place where it is reserved becomes a literally holy space, a place where we come before Christ, who is present there in a special way in which he is not present everywhere else.
That may well follow from the premise, but the premise is the very issue in dispute.
Now, since I of course believe in the omnipresence of God, and since all Christians believe in the omnipresence of God, and since the Bible expressly says that God dwells not in temples made with hands (Acts 7:48), it might be asked whether such a view is not either a) theological nonsense, meaningless, b) biblically utterly unprecedented prior to the controverted passages about the Lord's Supper, or even c) positively anti-biblical.
Depends on what we mean. Does Lydian think God is literally omnipresence? That God pervades or occupies physical space, like ether or subtle matter? Or is this a spatial metaphor for God’s omniscience and omnipotence?
But actually, I think there are foreshadowings and, to some extent, precedents in the Old Testament. For example, the Ark of the Covenant was definitely a place where God was present in a special way. That was why it had to be handled only by certain people and why even a well-intentioned handling by the wrong person could result in death (2 Samuel 6). That was why it was carried before the people when they marched (Joshua 3, Joshua 6). And that is why the Psalmist and other Scriptures repeatedly say that God "dwells between the cherubim" (I Chronicles 13:6, Psalm 80:1, Psalm 99:1, etc.). Hence, too, the Psalmist's repeated expressions of joy at the opportunity to go into "the house of the Lord" and be in God's presence (Psalm 27:4, Psalm 122). That, too, was why when the Ark was taken in battle a child born at that time was given a name that meant "the glory is departed from Israel" (I Samuel 4:22).
Then, too, the Mercy Seat (between the cherubim) was a place where blood was spilled on the Day of Atonement, which somehow was especially able to bring forgiveness for the people's sins (Leviticus 16:14). So the Mercy Seat was, as I have said of the Sacrament, a place where God, by His own special choice and commandment, interacted in a special way with His people.
This appeal fails to take into account the nature of cultic holiness or symbolic presence. For instance, the statuary cherubim represent actual cherubim, who “stand” in God’s presence, as sentinels guarding holy space. But just as the statuary cherubim aren’t real angels, by analogy, God doesn’t literally dwell between the statuary cherubim.
Keep in mind, too, that this is based on the conventional imagery of a divine council or heavenly court. That, itself, is picture language. It depicts God in anthropomorphic terms, as a seated monarch on his throne, surrounded by royal courtiers. But that, too, is a picturesque metaphor, which is based, in large part, on the paraphernalia of ancient Near Eastern kings.
Another example would be the Shekinah, which was a pillar of fire by night and a pillar of cloud by day. God led His people in this way. It was evidently a physical entity in which God was in some special sense present so as to help His people. In one of the most harrowing passages of the Bible, Ezekiel actually sees a vision of the Shekinah glory departing gradually from the Temple, illustrating God's judgement on His people (Ezekiel 10:18-19).
That certainly goes beyond artistic depictions. But how we understand that depends on what we think God is actually like. If God is not a physical being, then his “presence” is indirect. He can manifest himself through physical means. A physical medium which stands for God.
Lydia mentions the theophany in Ezekiel, yet the prophet is at pains to distinguish the theophany from God in himself: “Such was the appearance of the likeness of the glory of the Lord” (Ezk 1:28). Notice that this is three steps removed from the God himself. Not the Lord, but the glory of the Lord. Not the glory of the Lord, but the likeness of the glory of the Lord. Not the likeness of the glory of the Lord, but the appearance of the likeness of the glory of the Lord. God himself remains untouchable.
I want to dispose at once of the argument that Jesus could not have been speaking here of Holy Communion on the grounds that he hadn't yet ordained it. In fact, to speak of something important ahead of time, sometimes cryptically, is exactly the sort of thing Jesus did not infrequently. To give just a few examples, he prophesied his own resurrection by saying, "Destroy this temple, and in three days I will raise it up" (John 2:19), which the disciples understood only after the fact. He told Nicodemus (John 3) that he had to be "born of water and of the Spirit" and went on a bit about being "born of the Spirit," which wouldn't make a whole lot of sense until after the day of Pentecost.
i) The question is not whether Jesus can refer to something ahead of time, but whether the original audience was responsible for grasping a proleptic reference.
ii) Comparison with Jn 3 is counterproductive. Nicodemus was supposed to understand what Jesus meant. That’s because there were OT oracles about spiritual renewal, involving similar imagery (wind and water, e.g. Ezk 36:25-27; 37:1-14).
The similarity between what Jesus says in John 6 and the words of institution (quoted below) is far too striking for coincidence. I would go so far as to say that, with the words of institution in hand, we can see that Jesus must have been foretelling Holy Communion in John 6. The two fit together exactly as prophecy and fulfillment do. Jesus first tells them, bafflingly, that they must eat his flesh and drink his blood, and then later he hands them bread and wine and says, "This is my body; eat this" and "All of you drink this; this is my blood." What more do you want? The two things obviously refer to one another, which is to say that they refer to one and the same thing. It's just that, as with most prophecies, we only understand this fully after we see what the fulfillment looks like. Jesus must have known that his disciples would remember his earlier discourse when he spoke the words at the Last Supper. (Brief digression: John does not record the words of institution but does record the discourse on Jesus as the bread from heaven. The Synoptics record the words of institution but not the discourse. I believe that this is an instance of those undesigned coincidences that are the mark of eyewitness history, about which much has been said elsewhere. Were John writing an ahistorical literary work, he would very likely have included the words of institution.)
i) As Lydia herself admits, the imagery isn’t drawn from John’s account of the Last Supper.
ii) The contextual source of the imagery is threefold:
a) It’s not coincidental that this discourse comes on the heels of Jesus multiplying the fish and bread (Jn 6:1-15).
b) Christ’s opponents introduce the OT account of the manna in the wilderness, which Jesus picks up on and develops further.
c) The gruesome imagery foreshadows the account of the Crucifixion (Jn 19).
iii) It’s dissimilar to the words of institution. Jn 6 refers to “flesh” whereas the words of institution refer to the “body.” Since the words of institution are stereotypical or formulaic, we’d expect Jn 6 to reproduce the same ritualistic wording if it prefigured the Last Supper. Liturgical language uses the same words, same imagery. Ritual is repetitious.
iv) Jesus promises eternal life to whoever “eats his flesh and drinks his blood.” But on the sacramental interpretation, this would mean every one-time communicant is guaranteed salvation, including apostates. Yet that’s not consistent with Johannine theology.
v) Jn 6 treats “eating and drinking” as equivalent to “believing and coming” (vv35,40,47). That suggests the consumptive imagery is a figurative for having faith in Christ.
Lydia then devotes several paragraphs to expounding on the implications of the sacramental interpretation. But even if that’s valid, it’s only as good as her underlying interpretation.
The first point in this passage [1 Cor 11:23-32] that sits oddly with a memorialist position is the command that one examine oneself before taking Communion. Christians, at least those who have been carefully instructed at all about Communion, are so used to this requirement that we may take it for granted and not recognize the argument it presents against memorialism. Prior to this Paul has been talking about what we might call liturgical abuses connected with the meal that was apparently eaten prior to the Communion rite itself. (He brings this up after the quoted passage as well.) It would be somewhat easy to take phrases like "eating and drinking unworthily" to mean simply "eating and drinking disrespectfully." But Paul is going farther than just telling people to knock it off with the gluttony and behave respectfully during Communion. He's telling the believers to engage in introspection and not to receive Holy Communion until they have examined themselves and, I think we can take it, confessed their sins to God and resolved not to do them again. Why, if Communion is only a memorial? Do we have to undertake a special self-examination before participating in a Holy Week play? Yet that, too, commemorates Jesus' death. We sing songs in which we proclaim, show forth, remember the cross and Jesus' death, yet we aren't expected to undertake searching self-examination before each of those. It would seem overblown in the highest to speak of doing these things "unworthily" because we had not undergone a special examination of conscience before them.
This fails to make allowance for Paul’s play on words, as well as the ecclesiastical context. Although the “body” can symbolize the person of Christ, it can also symbolize the church. And, indeed, Paul is faulting some communicants for dishonoring their fellow church members by how they conduct themselves at the agape feast. In addition, to dishonor a Christian can indirectly dishonor Christ. Cf. R. Ciampa & B. Rosner, The First Letter To the Corinthians (Eerdmans 2010), 554-55
One more point about the words of institution. When Jesus says that this is the new covenant (testament) in his blood, he is alluding to a crucial ceremony in Israel's history. Moses (Exodus 24:8) took the blood of oxen and sprinkled it over the people after they had agreed to do all the words that the Lord had commanded in the Law. Moses said while sprinkling the blood, "Behold the blood of the covenant, which the LORD hath made with you concerning all these words." In instituting the Lord's Supper, Jesus institutes a new covenant between God and his people, and as blood was used for sealing the Old Covenant, so here, Jesus says that the cup is his blood which seals the new covenant. That seems to me, again, very strong language, and a rather surprising historical connection, for a bare memorial or symbol.
That’s because the cup signifies the death of Christ on the cross–which is perfectly attuned to a symbolic interpretation of the eucharist.