Matthew 6:24 (King James Bible) no man can serve two masters for either he will hate the one and love the other or else he will hold to the one and despise the other
The preposition for, the 1830 reading, is undoubtedly correct here. The printer’s manuscript reads or, an error that may have occurred as Oliver Cowdery copied the text from 𝓞 into 𝓟. Note that there is an actual or in the following clause, which probably prompted the error in transmission. Another possibility is that 𝓞 itself read or, the result of an error that occurred when Joseph Smith dictated the text to Oliver. Note that or and for sound alike, so perhaps Oliver misheard the for as or (especially if Joseph had just started to dictate the following clause with its beginning or as Oliver was supposed to be writing down the earlier for). In any event, the sequence “or either” is not really possible here.
Summary: Maintain the conjunction for in 3 Nephi 13:24, the 1830 reading and the reading in the corresponding Matthew passage; the or in 𝓟 is an early transmission error that produced for this context a virtually impossible reading, “or either”.