Paul's mention of "the baptism for the dead" has puzzled Christians for centuries. Do the earliest Christians have any insight for us?
Oddly enough, very little! It appears that they were as puzzled by Paul's statement as we are. They do, however, seem to be consistent where they do comment.
We have only Tertullian and John Chrysostom to work with. The editors of The Nicene And Post-Nicene Fathers apply 1 Cor. 15:29 in a note to a comment by Gregory of Nyssa, but I don't agree he is referencing the baptism for the dead. I will give you the comment and corresponding note anyway.
John Chrysostom (AD 347-407) is the most thorough commentator on the verse. He published Homilies on the Epistles of Paul to the Corinthians, and he did not dodge 1 Cor. 15:29. He even suggests that he has more to say on the subject, but cannot:
We have only two people to work with, but both say that "the dead" refers to our bodies. Our bodies are buried with Christ in baptism, and we are raised to new life in Christ. We also hope in the resurrection, when our dead bodies will either rise from the grave or, if we are still alive at his coming, be transformed instantly ("in a moment, in the twinkling of an eye") from corruptibility to incorruptibility.
I can't say I find that interpretation very satisfying. Paul seems to referencing a specific practice in that passage. I suspect he is talking about a rite that he disagrees with, performed by the gnostic teachers that he is refuting in that chapter.
Thus, I would paraphrase Paul's argument as: "If those gnostics don't believe in a resurrection of the body, why do they baptize on behalf of dead people? It doesn't make any sense."
I can't say I'm right. I'm just speculating. However, with just two early Christians, one writing 150 years after Paul and the other more than 300 years after, I think we are free to guess as well as they are.
Let's quote Tertullian in full, as his is much shorter.
The homily (sermon) from John Chrysostom is several paragraphs long, so I will just give you excerpts.
Chrysostom's homily begins with a description of what the followers of Marcion do. Marcion was the founder of a heretical sect that accepted only Luke's Gospel and a few of Paul's letters and only accepted those with edits. He rejected the God of Israel as different from the Father of Jesus.
Chrysostom scoffs at Marcion's practice, so that "none of the more exceedingly simple folk" be led astray, then turns to explaining the passage.
The mysteries are the bread and wine of the Eucharist which were given to converts immediately after baptism. The "response" is the rule of faith or "creed" that those who are being baptized confess to at their baptism. The Apostles Creed and Nicene Creed that many churches still repeat each week are products of the baptismal confession of early churches. These are the "awe-inspiring rules of doctrine" to which Chrysostom refers.
In the fourth century, "I believe in the resurrection of the dead" would have been a part of almost every church's rule of faith (creed). Tertullian points out in a much earlier writing that the original rule of faith, given by Jesus, was "in the name of the Father, the Son, and the Holy Spirit" (De Corona 3).
Finally we need to add the comment by the editors of The Nicene and Post-Nicene Fathers on a baptismal comment by Gregory of Nyssa (AD 335-395) from about the same time as John Chrysostom's. Again, I don't believe the editors are correctly referencing this to 1 Corinthians 15:29.
Gregory's comment concerns those who don't believe that Jesus is perfect. He says ...
The editors' note says:
There is a link there if you want to read the context of Gregory of Nyssa's words yourself. You'll have to search on the page I linked because that chapter is pretty long.
Only two early Christians, Tertullian and John Chrysostom, talk definitively about the baptism of the dead mentioned in 1 Corinthians 15:29. Both say that the reference is to our bodies, which are buried with King Jesus in baptism. Both say that we should understand this to mean that we live in expectation of the resurrection of our bodies.