The entire theme of Chapter 15 is the resurrection. If Christ did not rise from the dead, then all those souls that were baptized into the body of Christ, and had passed on, were not going to rise either.
So why are they (whosoever will) baptized into Christ’s dead body if there is no resurrection.
That is how 1 Cor. 15:29 harmonizes with the rest of the chapter, as well as with the scripturally recorded events of baptism, where only the living were baptized for their own salvation. It’s not a stand by itself verse saying some new doctrine.
Also notice that verse 30 starts with ‘And’, indicating the continued thought flow from verse 29:
“And why stand we in jeopardy every hour?”
Paul (whom had already been baptized years earlier) says ‘they’ in vs 29 because he’s writing to the saints in Corinth, who have already been baptized; so, ‘we’ does not apply in that context, but does in vs 30.
Zuriel, you are correct. It would be like what I did below. If you take out the versus after v20 and before v29 it becomes a little clearer. And no, I don’t change the meaning by taking these two verses by themselves.
20But Christ has indeed been raised from the dead, the firstfruits of those who have fallen asleep.
29Now if there is no resurrection, what will those do who are baptized for the dead? If the dead are not raised at all, why are people baptized for them? (In other words why would people be baptized for a dead person?)
The phrase “what will those do who are baptized for the dead?” is asking, if Jesus had not risen from the dead the people who had been baptized would have been baptized for some dead person and it would do them no good.
Unfortunately the Mormons have interpreted this to mean that they can be baptized in the place of some dead person.