Karl Franson suggests (personal communication, 2 October 2003) that in this passage the with should be removed to read “drinking in the traditions of the Lamanites”. 𝓞 is not extant here, but spacing between extant fragments suggests that with was in 𝓞. There are no other occurrences of “to drink in” in the Book of Mormon text. There is one occurrence in the King James Bible, and it occurs without the with: “the earth which drinketh in the rain that cometh oft upon it” (Hebrews 6:7).
Under definition 4 for the verb drink, the Oxford English Dictionary lists the meaning for “to drink in” as ‘to take into the mind, especially by the eyes or ears, with the eager delight of one who satisfies physical thirst’, but all the citations there lack the preposition with. However, the OED online does list one example of this usage under the noun nourice ‘nurse’ (here I regularize the spelling but retain other accidentals):
The critical text will therefore maintain in Alma 47:36 this unique instance in the Book of Mormon of “to drink in with” since it is the earliest reading and there is evidence for the phraseology in earlier English.
Summary: Maintain in Alma 47:36 the occurrence of with in the present participial clause “drinking in with the traditions of the Lamanites”, the reading of all the (extant) textual sources.