Apparently it was John Gilbert, the 1830 compositor, who deleted the not here. The crossout is precisely like the crossout of with found a few verses later in 2 Nephi 27:2. (The crossed-out not is on line 17 of page 85 of 𝓟, while the crossed-out with is on line 26.) We know that the later crossout (of the with) is Gilbert’s because the supralinearly inserted of looks precisely like the of that he later inserted in Alma 51:7; there he emended “many the people of liberty” to “many of the people of liberty” (see the discussion under Alma 51:7).
Here in 2 Nephi 26:32, the earliest text has a sequence of eight occurrences of the same phraseology (“that they should not”), preceded by an initial “that men should not”. Clearly, one could view the last occurrence (“that they should not do none of these things”) as an error—that is, one could presume that the not was accidentally added because of the preceding eight occurrences of should not. On the other hand, multiple negatives (also known as double negatives when only two negatives are involved) are found in the original text, as in the following examples:
(Note, in particular, the examples in 3 Nephi 17:17 and Ether 12:6; there the 1830 compositor is the one responsible for deleting the extra not.) These four examples are all similar to the example here in 2 Nephi 26:32 in that each one involves a not following either none or no. In each case, the not has been removed by editing.
Interestingly, there is evidence that the manuscript scribes and even the 1830 compositor himself sometimes created multiple negatives:
So it is possible that the five cases where the earliest sources support the multiple negative could be due to dialectal interference during the early transmission of the text.
Even so, the critical text does not necessarily favor standard English. Instead, in each case of negation, we allow the earliest textual sources to determine whether the multiple negative should be included in the original text. When supported by the earliest reading, the critical text will accept multiple negation, despite its unacceptability in standard English.
For examples of multiple negation involving the negative conjunction nor, see 2 Nephi 23:17. For examples of multiple negation involving the prepositional but, see 1 Nephi 14:28. And for a complete discussion, see negation in volume 3.
Summary: Accept the original multiple negative in 2 Nephi 26:32 (“and that they should not do none of these things”); in this instance, the 1830 compositor removed the not.