The Spirit is more than only the agent of our baptism into the Body of Christ; He is also the living Fountain at which we all drink and are refreshed (cf. John 4:14; 7:37-39). — Stam, page 214.
The stress in verse 13 is on “all” and “one.”
This difficult passage [v.13] evidently looked back to the definite moment of time when the Jews and Gentiles in Corinth were saved, as appears from the verb [were all baptized], which is the first aorist of the first person plural passive to indicate that there was a definite nick of time when this put the Jews and Gentiles of Corinth into the one Body. This happened evidently in the year 53 A.D., when he came to Corinth and led many Jews and Gentiles to Christ. Then the risen Lord breathed invisibly His Spirit into them and baptized, submerged, identified them forever by His Spirit into His death, burial and resurrection. This put all the believing Jews and Gentiles into His Body, which, as far as the story in Acts goes, was still hidden in the Jewish Pentecostal regime. — Bultema, page 101-102
Being born of the Spirit gives us a new life. Being baptized by the Spirit gives us a new place. This new place is in the Body of Christ. Both the birth and the baptism are simultaneous but they are not similar. There was a time, however, when there were people who were born again of the Spirit but were not indwelt by the Spirit.
The result of this baptism is not said here to be speaking in tongues, or ecstatic experiences. It meant a common unity. Jews were no longer Jews as such. Gentiles were no longer Gentiles as such. Slaves were no longer slaves as such. All lost their former standing in the flesh and all found a new standing in the Spirit. There were, henceforth, no castes nor classes. There was a new oneness of life and identity.
A further result of this baptism by the Spirit was not an organization but an organism. It resulted in the forming of a body — the Body of Christ. — Laurin, page 214
To determine the ultimate purpose of this “baptism” and its consequent and recurrent “filling,” we have but to inquire as to the purpose of the coming of the Holy Spirit. It was … to exalt Jesus Christ. It was to continue Christ’s ministry both in us and through us. Our baptism into Christ’s body means the Spirit’s presence in our body. His presence there is to produce Christlikeness. It is to endow us with gifts and graces that will furnish us with both ability and character for the beautiful life. — Laurin, page 215.
The Church, which is the body, is not the exclusive possession of any particular people. In fact, men have nothing to say about entrance into this body of believers. This is the prerogative of the Holy Spirit. Having once entered the body by birth and baptism, we function in the given sphere of our membership.’
The membership spoken of here is not creedal membership but organic membership, for “the body is not one member but many.” It is our individual relationship to collective Christianity within the organism of Christ’s body.
The membership of this mystical body of Christ is being addressed for the purpose of indicating its inter-related capacities and functions. It is asked to look at itself not as a body alone but as individual parts as well. These parts are to consider themselves in relation to every other part and are to adjust themselves in both spirit and service so that the whole body will function with precision. — Laurin, page 216.
There’s a lot of disagreement on this passage, some of which was reflected in my commentaries, but I don’t find it difficult. The Spirit gives out gifts individually, so all believers won’t have the same gifts. But we’re all supposed to work together as one body in Christ, each using our own gifts so together we accomplish the work which is God’s will for the Church.
In Christ, in this dispensation, there is not Jew or Gentile. Whether the individual believers in Corinth understood all this at the time they were saved isn’t really an issue for me. Most people who are saved today don’t understand it all right off either. Maybe Paul didn’t even understand it fully at the time when he spoke in Corinth, and that’s probably part of the reason why he’s explaining it so fully here.