The NIGCT commentary listed three common understandings:
1) distinguishing between the sacred eucharistic elements of the Lords body and ordinary bread from the table. This is a common historical view among Catholics and some Protestants, including Reformed. He doesnt cite any modern critical commentators as holding that view.
2) to respect for the congregation of believers as the body of the Lord. This is held by many current interpreters, including my other commentary (Anchor Bible).
3) Right judgment extends to what it means to be identified with, and involved in, the cross of Christ, in anticipation of judgment. In this sense our verse states that they must recognize what characterizes the body as different, i.e., be mindful of the uniqueness of Christ, who is separated from others in the sense of giving himself for others in sheer grace. This is the view of the NIGCT commentary.
What question was Paul answering by this comment? The context was a church where people were apparently eating individually, without proper concern for others. There is also a suggestion of factions. The problem wasnt that people held the wrong theology of the Real Presence, so that for example they thought the presence was only symbolic or only spiritual. Rather, their attitudes didnt take Christ seriously, however he is present. I think either of (2) or (3) would be consistent with the context.
I would say that Calvins commentary gets the sense correctly, probably based on sense (3).
He adds the reasonbecause they distinguish not the Lords body, that is, as a sacred thing from a profane. They handle the sacred body of Christ with unwashen hands, (Mark 7:2,)2 nay more, as if it were a thing of nought, they consider not how great is the value of it.3 They will therefore pay the penalty of so dreadful a profanation. Let my readers keep in mind what I stated a little ago,4 that the body5 is presented to them, though their unworthiness deprives them of a participation in it.
In case you havent heard it before, heres an argument for 2, from the Anchor Bible:
The corporate significance of the meal has already been introduced at 10:16 (cf. supra, pp. 250253). The term body was applicable to the Passover societies that were formed for the festival; the group joining in the meal became a new kind of entity with such a close binding connection that all of the persons are members of each other (an idea which Paul develops in 12:1226). This idea grips his mind, for he elsewhere calls the church the body of Christ (Rom 12:5; 1 Cor 12:13, 27; Eph 1:2223, 4:4, 12, 16; Col 1:18, 2:17, 3:15). He thought of the body of Christ as present, active, and purified for his manifestation to the world after he was no longer present in the flesh. The body in which he is now present is the body of believers. Paul regularly refers to the physical, historical existence of Jesus Christ on earth by the term flesh (sarx; cf. Rom 1:3, 9:5; 2 Cor 5:16; Col 1:22; etc. The only possible exception is Rom 7:4, and the intent there is possibly a double meaning.) Body, then, in this passage may be understood to refer to the church, here recognized in its chief act of common worship, the Lords Supper.
This argument seems compelling to me. It has been criticized because it uses body differently than in version 27. But in 27 he uses body and blood, where in 29 only body.
Fee (NICNT) takes a variant of (2), seeing 27-28 and 29-30 as referring to different abuses. He sees a reference to 10:17, which sees body as reflecting the believers, and particularly their unity. Note that 10:16-17 show exactly the transition from Christ's body and blood to the body of believers. That seems a convincing response to the objection.
(I also checked Hermeneia. They don't deal with this question at all, which seems pretty weird.)