Amulek clarifies the problem. He is not saying that the Messiah will not save. He will. The difference is that the Messiah can save only upon principles of repentance. The unrepentant cannot be saved. The argument Amulek offers is that “no unclean thing can inherit the kingdom of heaven.” Amulek uses the phrase apparently believing that it is accepted and understood.
We do see a similar phrase in 1 Nephi 10:21 which says that “no unclean thing can dwell with God.” This phrasing does not appear in the Bible, but it is related to the concepts of clean and unclean under the law of Moses. The Nephite phrasing might be derived from Isaiah 52:10–11: “The Lord hath made bare his holy arm in the eyes of all the nations; and all the ends of the earth shall see the salvation of our God. Depart ye, depart ye, go ye out from thence, touch no unclean thing; go ye out of the midst of her; be ye clean, that bear the vessels of the Lord.” Although Isaiah doesn’t mention entering God’s presence directly, the vessels of the Lord are in the temple, and, therefore, symbolically in the presence of God.