An old argument against the Book of Mormon is that no self-respecting Hebrew would even think of building a temple outside of Jerusalem as Nephi did in the New World. Since Hugh Nibley’s day that argument has been handled by pointing out that legitimate Jews at Elephantine, Egypt had built their own temple for worship there, and even had some degree of approval from authorities in Jerusalem. See my Book of Mormon Nugget, “Lessons from the Elephantine Papyri Regarding Book of Mormon Names and Nephi’s Temple.” Richard Friedman’s Who Wrote the Bible? is also of interest, among many other sources, on the evolution of the notion of centralized worship only in Jerusalem.
A related issue came up in an LDS doubter’s list of reasons for rejecting Nephi’s account, for he argued that Lehi would not have built an altar and offered sacrifices as Nephi described (my response in “Joseph and the Amazing Technicolor Dream Map: Part 1 of 2” at The Interpreter also includes a reference to Elephantine).
Recently I learned of a useful resource that lists a variety of Jewish temples and other holy places outside of Jerusalem, with most mentioned in some way in the Bible, supporting the notion that the centrality of worship decreed in Deuteronomy is not the end of the story of widespread and non-blasphemous worship outside of Jerusalem in ancient Israel. See “Israelite Temples outside Jerusalem” at the Pronaos Blog. The list is bigger than I realized. Worth reviewing.