Renegade's first question has to do with the question of "alien immersion" - that is, many Baptist churches have a policy that if the candidate for membership was already immersed in a church that is not Baptistic, they will not recognize that baptism. If they did recognize such baptisms, this would imply recognition that it was administered by a true church, which in turn would imply that they logically are agreeing to grant letters of transfer for their own members to join such a church. As a matter of principle, there are many Baptist churches who will not recognize baptisms from a non-Baptistic church. Most denominations, not just Baptists, have some restrictions and regulations as to what baptisms they will or will not accept. The Roman Catholic Church and the United Methodist Church will not accept Mormon baptism because the LDS church is non-trinitarian. I don't think this is the issue that Paul is dealing with in Ephesians 4:5 or1 Corinthians 12:13.
Renegade's second question is with regard to Baptist churches that re-baptize folks who were previously baptized in an unsaved condition. Many Baptist churches have a policy that baptisms administered to a person who was later found to be unsaved are declared to be "null and void." Since baptism must be preceded by salvation, the newly saved person should be re-baptized, which is regarded as their actually receiving scriptural baptism for the first time. The accusation has been made that churches that re-baptize their members who "get saved" again are motivated by a desire to pad their baptism statistics, but I don't think we have a right to make that kind of judgment. Here again, this practice is not what Paul is talking about.
So, what is Paul's point when he says "one baptism?" In the context, Paul is emphasizing the need to
"keep the unity of the Spirit in the bond of peace" (Ephesians 4:3). The Ephesian church was composed of both Jews and Gentiles, but God had broken down the walls of division between those two ethnic groups (Ephesians 2:11-14). They now had a oneness of faith, based around acceptance of one Lord, one faith, one form of baptism, one God and Father of all.
Pulpit Commentary on 1 Corinthians 12:13:
"We were all baptized. Whether we be Jews or Gentiles, whether we be bond or free. Moreover, as these were national and social differences, they were all obliterated by baptism, which made us all equal members of one holy brotherhood (Galatians 3:28)."
Gill's Commentary on Ephesians 4:5:
"There is but one baptism, literally and properly so called, which is water baptism; and which is to be administered in one and the same way, by immersion in water; and on one and the same subjects, believers in Christ; and in one and the same name, the name of the Father, the Son, and the Holy Ghost; and to be performed but once, when rightly administered." (Gill appears to recognize the propriety of re-baptism for those whose previous baptism was not "rightly administered)." Most Baptists would say that baptism that is not administered by a scriptural church, or was administered on an unsaved subject, was not "rightly administered."
