Baptized for the Dead.

Paul is talking about life after death in the prior verses. then he says this:
Otherwise, what will those do who are baptized for the dead? If the dead are not raised at all, why then are they baptized for them?

But do not stop there read father and you will see something interesting.

Otherwise, what will those do who are baptized for the dead? If the dead are not raised at all, why then are they baptized for them? 30 Why are we also in danger every hour? 31 I protest, brethren, by the boasting in you, which I have in Christ Jesus our Lord, I die daily. 32 If from human motives I fought with wild beasts at Ephesus, what does it profit me? If the dead are not raised, let us eat and drink, for tomorrow we die. (1 Corinthians 15:29-32).

When that verse comes in Paul is speaking with the words that refer to others who do this practice, by using the word "those" and then "they", then Paul moves on to speak of the Christians and uses the word "we" and then "I".

Also Paul calls Jesus Our Lord. Not any reference to them being any part of US

There were other religions that the Corinthians were aware of at the time that Baptized for the dead and Paul was making a reference to their Practice, not the practice of the Christians, to draw a conclusion of life in the Body after the death of the Body.

Now some off track religions make this a practice without studying the religions around Corinth based soley on one reference to Baptizing for the dead. This is how cults come into existence, when one educated person who has a form of religion gets his teeth sunk into a verse and builds a church. somewhat like the Morman/Latter days got their start.