The italicized section of 2 Nephi 26:33 is the part that is parallel to Galatians. What is most interesting is not the correspondence of bond/free, male/female, Jew/Gentile (Greek) but the addition of black/white in the list.
If I can start with my exegetical assumptions:
With those two bases, I have to ask what there is on the plates that underlies the black/white contrast in 2 Nephi 26:33.
First, the black/white contrast should not be metaphorical. This isn't a distinction between good and bad, though light and darkness have been used to reflect the good/bad pair. If it were actually a metaphor for good (people) and bad (people) we might have expected the light/dark, but not the black/white.
Second, the rest of the verse so clearly speaks of people (male/female, Jew/Gentile, bond/free) that one must suppose that for literary consistency, the black/white must also represent a paired opposition of people.
Third, the black/white opposition does not reflect actual skin color distinctions in any known ancient New World population. Even taking "white" to be associated with the Lehites (a stretch in color value distinctions) the "black" does not fit what is commonly called the "red" man. What we have, then is a color match that attaches to people, but is not descriptive of skin color. What might be meant, and what might be Nephi's frame of reference?
The only way I can interpret this pairing is to return to the clear presence of Joseph Smith's intrusion of vocabulary in this verse. It is impossible to see this verse as a literal, word-for-word translation of the plate text completely separate from Galatians. The close correspondence of vocabulary is sufficient to understand that Joseph's knowledge of the language of Galatians has shaped the translation of the meaning of the plate text at this point.
With this evidence of Joseph's vocabulary providing meaning for the plate text, I suggest that the black/white pairing also comes from Joseph's vocabulary and cultural context. Rather than a distinction of color, however, I suggest that the intent of the use of the color terms is to denote race rather than skin color. Thus Joseph's understanding of "blacks" and "whites" as race rather than just color informs Nephi's meaning. Nephi is not describing skin color, but a separation of races.
Once again, this is highly suggestive that Nephi's community had struggled with the question of integration, not only of gentiles, but gentiles of another race. Nephi's plea for inclusion specifically involves race, rather than just gender (male/female), religion (Jew/Gentile), or social status (bond/free).