As with all key phrases in the scriptures, the phrase "salt of the earth" is used consistently to describe a certain group of people. There are other key words and/or phrases that are used in connection with the phrase "salt of the earth" such as covenant, savor, saviors of men, trodden under foot of men, cast out, light, gentiles and the house of Israel, which help to define who are the salt of the earth, what their role is and what is prophesied concerning them.
D&C 101:39-40 tells us who are the salt of the earth, and what they are called to be. "When men are called into mine everlasting gospel, and covenant with an everlasting covenant, they are accounted as the salt of the earth and the savor of men; they are called to be the savor of men; therefore, if that salt of the earth lose its savor, behold, it is therefore good for nothing only to be cast out and trodden under the feet of men."
President Benson clearly taught that references to the salt of the earth in the D&C referred to Church members of this last dispensation. In CR April 1985, Ensign 15 (May 1985), he said:
"The Lord said to the Church members of this dispensation: 'But inasmuch as they keep not my commandments, and hearken not to observe all my words, the kingdoms of the world shall prevail against them. For they were set to be a light unto the world, and to be the saviors of men; and inasmuch as they are not the saviors of men, they are as salt that has lost its savor, and is thenceforth good for nothing but to be cast out and trodden under foot of men' (emphasis added).
Salt is linked with light. In 3 Nephi 12, the Lord said to the people "...I give unto you to be the light unto this people." This is said immediately after saying "...I give unto you to be the salt of the earth." Light and salt are therefore linked by the words 'ye are' and the Lord in the Sermon on the Mount says "Ye are the salt of the earth," and in the next verse He says "Ye are the light of the world." This connection is made even clearer in D&C 103:8-10 wherein the Lord tells the Church members, or those who have entered into the covenant, that "they were set to be a light unto the world, and to be the saviors of men; and inasmuch as they are not the saviors of men, they are as salt that has lost its savor."
The idea of being saviors of men is also introduced. Since we know that men can be saved only in and through the Savior, being saviors of men implies that we bring people to Christ to be saved. The Lord also makes it clear that in order to be saviors of men ye must "...hold up your light that it may shine unto the world. Behold I am the light which ye shall hold up..." (3 Nephi 18:24).
The phrase 'trodden under foot of men' is used with the phrase salt of the earth to denote the consequences of the salt of the earth losing its savor. Both 3 Nephi 16:15 and 3 Nephi 20:16 are prophecies concerning the salt of the earth (members of the Church), and also tell us that it will be the House of Israel that shall tread down the salt that hath lost its savor. This is a reversal of the Gentiles coming to America and casting out Lehi's descendants (who are of the House of Israel) and treading them down. It is the Gentiles in the latter days who are to be cast out and trodden under the feet of the House of Israel. Since these references makes clear that these Gentiles shall become as the salt of the earth which has lost it savor and is good for nothing but to be trodden under the foot of men, the Lord is prophesying what will become of many who have entered into the covenant. (3 Nephi 16:15) These are those who have received the Gospel but rejected the fulness of the Gospel. (3 Nephi 16:10), or those who have not repented, thereby linking the failure to repent to the salt losing its savor. "And thus commandeth the Father that I shall say unto you: At that day when the Gentiles shall sin against my gospel, and shall reject the fulness of my gospel, and shall be lifted up in the pride of their hearts...; and if they shall do these things and shall reject the fulness of my gospel, behold, saith the Father, I will bring the fulness of my gospel from amng them" (3 Nephi 16:10 emphasis added).
The prophecies in 3 Nephi 16; 20 & 21 concerning the Gentiles who are the Salt of the Earth are quite clear in that there is no question but that many of the Salt of the Earth (members of the Church) will reject the fulness of the Gospel, reject God's words which have been revealed unto them, and because they refuse to repent, will be trodden down under foot by the House of Israel.
In an end time context, those "cut off" include wild branches of the olive tree (Gentiles) who do not "continue in his goodness" (Romans 11:22; cf. Jacob 5-65-66), "whosoever will not believe" the words of Christ, which the Lord's "servant" will bring forth to the Gentiles (3 Nephi 21:10-11); cf. Isaiah 52:13-15), "whosoever will not repent and come unto my Beloved Son" at that time (3 Nephi 21:20), and those who "will not hear the voice of the Lord, neither the voice of his servants, neither give heed to the words of the prophets and apostles" when the "arm of the Lord" is revealed (D&C 1:14; cf. JS. Matt. 1:55; JS-History 1:40).
In this end time setting, the Lord's "servant" who brings forth the words of Christ to the Gentiles, is also "like unto Moses." Jesus says of those who disbelieve his words at that time, "(It shall be done even as Moses said) they shall be cut off from among my people who are of the covenant (or the Salt of the Earth)" (3 Nephi 212:11).
This test may help you determine which of the Gentiles you are apart of. To whom is Nephi speaking when he says "A Bible! A Bible!"? Of the two ways in which we can interpret this prophecy, do we accept what the Book of Mormon is actually telling us or do we subscribe to current popular opinion? From what Nephi has seen when viewing our day, it seems evident that we "who are identified with the Gentiles" (D&C 109:60), are particularly vulnerable