Antidoron

Admission to Communion Implies Right Faith. Therefore, the question is what is Right Faith? Nobody said it better than Moss.

• He who communicates at a Roman altar declares by doing so that he accepts the papal claims and the decrees of Trent and the Vatican.
• He who communicates at an Orthodox altar declares by doing so that he accepts the decrees of the Seven Ecumenical Councils and all the teaching of the Orthodox Communion.
• He who communicates at an Anglican altar similarly declares by doing so that he accepts the teaching and the authority of the Anglican churches.

The teachings of the English church are, however, mostly negative in character:

The Anglican Communion is not committed to any particular doctrine of the Eucharist ...
No such doctrine can be proved from Scripture.
The Universal Church has defined no such doctrine.
The outward visible signs, the bread and wine, are really bread and wine.
The Body and Blood of Christ are really the Body and Blood of Christ.
To deny either truth is "to overthrow the nature of a sacrament".
That is rejected by the Anglican Communion, and that alone.

Conformance to that given in red above means rejecting Transubstantiation (Roman), Consubstantiation (Lutheran), Receptionism (Calvinist), and many, many more speculative theories and theologies. And sharp rejection does not imply openness to anything.

The most relevant article is as follows:

Article XXVIII

Of the Lord's Supper

The Supper of the Lord is not only a sign of the love that Christians ought to have among themselves, one to another, but rather it is a sacrament of our redemption by Christ's death: insomuch that to such as rightly, worthily, and with faith receive the same, the bread which we break is a partaking of the body of Christ, and likewise the cup of blessing is a partaking of the blood of Christ.

Transubstantiation (or the change of the substance of bread and wine) in the Supper of the Lord, cannot be proved by Holy Writ, but is repugnant to the plain words of Scripture, overthroweth the nature of a Sacrament, and hath given occasion to many superstitions.

The body of Christ is given, taken, and eaten in the Supper, only after an heavenly and spiritual manner. And the mean whereby the body of Christ is received and eaten in the Supper is faith.

The Sacrament of the Lord's Supper was not by Christ's ordinance reserved, carried about, lifted up, or worshipped.

De Coena Domini

Coena Domini non est tantum signum mutae benevolentiae Christianorum inter sese, verum potius est sacramentum nostrae per mortem Christi redemptionis. Atque ideo rite digne et cum fide sumentibus, panis quem frangimus est communicatio corporis Christi: similiter poculum benedictionis est communicatio sanguinis Christi.

Panis et vini transubstantiatio in Eucharistia ex sacris literis probari non potest, sed apertis Scripturae verbis adversatur, sacramenti naturam evertit, et multarum superstitionum dedit occasionem.

Corpus Christi datur, acciptur, et manducatur in Coena, tantum coelestis et spirituali ratione. Medium autem quo corpus Christi accipitur et manducatur in Coena, fides est.

Sacramentum Eucharistiae ex institutione Christi non servabatur, circumferebatur, elevabatur, nec adorabatur.

But nothing here says "anything goes," or "all views are equally acceptable." 'Thin' is not at all the same as 'weak'. Therefore, these sorts of complaints are a bit overblown:

... the party that asserted comprehension of all outliers at once was in fact the dominant notion from the beginning. As Kinsman put it in Salve Mater, “Like many others, I attached Highest importance to the doctrines of Baptismal Regeneration, the Real Presence in the Holy Eucharist, of the Eucharistic Sacrifice, of the sacramental character of Confirmation and Penance. All these doctrines the Church tolerates; but so long as equal toleration is given to others of a different or even neutralizing sort, this is not definitely to teach them. To tolerate everything is to teach nothing.”

Corpus Christi datur ... tantum coelestis et spirituali ratione. But spirit is not less real than body (it is not the case that real = corporeal): it is more real (from both a Platonic and a Christian perspective). And in that fashion it really is given.

As even Aquinas noted, Christ's "presence" in the sacrament cannot be "as if in a place" and, as Newman averred, in an eucharistic procession Christ's body is nonetheless "not moved." Or, perhaps, even as the Lady Elizabeth said,

He gave his Flesh, and Blood in Bread and Wine:
For if his Body he did then divide,
He must have eat himself before he dyd.