As explained under Alma 43:45, the original text had no instances of the word rite(s), even though the word right(s) was often spelled that way in the manuscripts (and for three readings in some of the printed editions). Here in 3 Nephi 2:12, Oliver Cowdery initially wrote rights in 𝓟, but later (with somewhat heavier ink flow) he corrected the word to rites. The original manuscript may have read as rights or rites; for extant portions of 𝓞, there are four with rights and six with rites. Except for Hyrum Smith’s misspelling in 𝓟 of wright(s), the 1830 compositor set instances of rite(s) and right(s) according to his copytext, which suggests that in 3 Nephi 2:12 𝓞 read rights. Of course, the issue here is which reading works best in context, not what 𝓞 read. The 1908 RLDS edition, in accord with the corrected reading in 𝓟, replaced the correct rights with rites. The critical text will maintain rights in 3 Nephi 2:12 and elsewhere in the text. For a complete analysis of these two words in the Book of Mormon text, see under Alma 43:45.
Summary: Maintain in 3 Nephi 2:12 the word rights, not the secondary rites that occurs as the corrected reading in 𝓟.