How do denominations which do not believe in transubstantiation, view 1 Cor 10 : 16-17?

A definition of transubstantiation in a Reformed Protestant book is:

"Change undergone by the physical elements of the Eucharist, according to Roman Catholic teaching. The bread and wine, in this view, materially change into the body and blood of Christ, although the accidents of the bread and wine (their appearance, taste, and smell, for instance) remain unchanged." (Pilgrim Theology p.472, Michael Horton, Zondervan, 2011)

Trusting that such a definition is acceptable, I will quote further from the same book, where it explains the Reformed Protestant reasons for not viewing the communion elements the same way.

"Against views of deification suggesting that creatures somehow merge with God's essence or teaching that grace is a created substance infused into the soul [ft.46], the Reformers insisted that in salvation the gift is Christ - the God-Man himself. We cannot receive Christ's gifts, Calvin argued (along with Luther) without receiving Christ himself.

Ft.46 This is the ontology that supports the dogma of transubstantiation, according to which bread and wine no longer retain their creaturely essence but become the divine body and blood, worthy of adoration. However, with the middle category of energies, God's gracious working ("the powers [dynameis] of the age to come" Heb.6:5) may be seen as divine action without being collapsed into the divine essence; the rays, but not the sun. We do not worship the Bible, baptism, or the Lord's Supper, but we also do not regard them simply as created things. United to God's activity, they are means of grace. Similarly, believers are never sharers in the divine essence, but they are made beneficiaries of God's gracious energies, glorified to the degree that creatures can ever be like God." (Ibid. p.337)

This raises the point as to how believers 'receive Christ'. Reformed Protestants believe that happens at the point of saving faith in Christ as Saviour and Lord; the repentant criminal on a cross next to Jesus might be a good example of him 'receiving Christ' by faith alone, without benefit of any sacraments. Now follows explanation about distinguishing between sign and reality, following after details about two extreme positions (that baptism and the Supper "are basically human and not divine acts" and that of collapsing distinctions between sign and reality):

"The sign simply is (or becomes) the reality itself, as in the Roman Catholic doctrine of transubstantiation, in which the creaturely substance of bread and wine is annihilated. Grace elevates nature beyond itself, transforming it into something supernatural... Though differing sharply from the Roman Catholic as well as the Luthern position, the Reformed view is nevertheless in agreement with the catholic heritage, over against Anabaptist traditions, in regarding the sacraments as objective means of grace. As Francis Turretin put the matter, 'The question is not whether or not the sacraments are efficacious in some sense. This is granted by both sides. The question is how they exert their efficacy'." (Ibid. pp.358-9)

Now comes the scripture text in question. First, the context is examined, starting from verse 1, to see how covenant and idolatry and circumcision (as a sign of the covenant) relate to Christian sacraments:

"Circumcision was the 'seal' of their justification (v. 11). Similarly, an adult convert is justified the moment he or she trusts in Christ, but this justification is sealed or ratified by baptism. The choice, then, is not between salvation by grace through faith and salvation by sacraments; the latter signify and seal the former. Precisely for that reason, they must not be withheld from entitled recipients. In fact, withholding the visible sign and seal excommunicates one from the visible covenant Community" (Ibid. p.362)

1 Corinthians 10:1-22 is then invoked as providing that dire warning. Further, vss.1-4 are quoted to show how Israel kept participating in the redemptive acts in their history, how those who left Egypt "were baptized into Moses in the cloud and in the sea," and drank of the rock in the wilderness, "and the Rock was Christ." The book then goes on to explain what it means for the signs to 'participate' in the reality they signify.

Conclusion: The bread and wine combine as a sign of Christians being in the new covenant, in Christ, but a sign is not that which it signifies. A sign points to the reality - in this case, Christ. Likewise, biblical language about the one loaf speaks of "the [one] body of Christ" which is comprised of every member of his Church, his 'bride'. Therefore the bread is a sign pointing to being a part of that spiritual 'body of Christ', which is one symbolic body. The wine is language about the shed blood of Christ, communion wine being the sign pointing to how Christians are cleansed by that shed blood. Literal, physical objects are exquisitely simple signs of the most profound spiritual realities for Christians: the body and blood of Christ, broken and shed for us. It's almost too awesome for words, yet the Bible simply uses words about simple elements to stagger us with their symbolic realities.