It is by no means obvious that to be baptized for the dead means to be baptized as a proxy for a deceased persons. Not obvious. There’s a case to be made for that interpretation, to be sure, but it does not hold a monopoly on plausibility. For instance there is a way of reading it that actually implies a repudiation of such a possibility. Since the verse in Greek contains no punctuation, one could translate it this way:
*Now if there is no resurrection, what will those do who are baptised? [Is it] for the dead? If the dead are not raised at all why are people baptised? for them?
*
In this way, the verse could be read as presupposing the absurdity of such a baptism, and using that in the argument. While this is an admittedly offbeat reading, it has some real scholarly support, as was argued in a very intelligent doctoral dissertation by Bernard Foschini in 1951.
But even if we take the text as it stand in most translation (and I do incline to stick with the standard ways of translating it) there are still score of questions a serious person can ask: Does Paul refer to Christian baptism or to oblations in general? If he means baptism, does “for” even mean “for the sake of”? If it it does, does the benefit of such baptisms for dead people consist in them receiving the actual grace of baptism themselves? I could write a pretty long list of meaningful difficulties that exegetes have found in interpreting this text. That is not to say the Mormon position is not defensible, only that it does have an automatic claim to be preferred over others. Even the unlikely argument that Paul is speaking with disapproval of a non-Christian practice is a plausible contender. It would logically fit his argument if he is criticizing the practitioners of it for hypocrisy, saying something like, “They deny the resurrection, but their own practices make no sense apart from that.”