Those living a terrestrial life will be on the earth during the Millennium. Many prophets have spoken about this idea, that people of all faiths will be on the earth during the reign of the Savior Jesus Christ.
Brigham Young said:
When all nations are so subdued to Jesus that every knee shall bow and every tongue shall confess, there will still be millions on the earth who will not believe in him; but they will be obliged to acknowledge his kingly government. (Discourses of Brigham Young, p.115)
In the Millennium men will have the privilege of their own belief, but they will not have the privilege of treating the name and character of Deity as they have done heretofore. No, but every knee shall bow and every tongue confess to the glory of God the Father that Jesus is the Christ. (Discourses of Brigham Young, p.119)
Joseph Fielding Smith stated:
Some members of the Church have an erroneous idea that when the millennium comes all of the people are going to be swept off the earth except righteous members of the Church. That is not so. There will be millions of people, Catholics, Protestants, agnostics, Mohammedans, people of all classes, and of all beliefs, still permitted to remain upon the face of the earth, but they will be those who have lived clean lives, those who have been free from wickedness and corruption. All who belong, by virtue of their good lives, to the terrestrial order, as well as those who have kept the celestial law, will remain upon the face of the earth during the millennium. Eventually, however, the knowledge of the Lord will cover the earth as the waters do the sea. But there will be need for the preaching of the gospel, after the millennium is brought in, until all men are either converted or pass away. In the course of the thousand years all men will either come into the Church, or kingdom of God, or they will die and pass away. In that day there will be no death until men are old. Children will not die but will live to the age of a tree. Isaiah says this is 100 years. When the time comes for men to die, they will be changed in the twinkling of an eye, and there will be no graves. (Doctrines of Salvation, 1:86)
Neal A. Maxwell said:
We understand, of course, that there will be many nonmembers of the Church living during the Millennium, but there will be a clear willingness by all the good and decent men and women of all the races, creeds, and cultures to abide by a terrestrial law. (Sermons Not Spoken, p.81)
Bruce R. McConkie wrote:
Thus there will be many churches on earth when the Millennium begins. False worship will continue among those whose desires are good, “who are honorable men of the earth,” but who have been “blinded by the craftiness of men.” (D&C 76:75.) Plagues will rest upon them until they repent and believe the gospel or are destroyed, as the Prophet said. It follows that missionary work will continue into the Millennium until all who remain are converted. Then “the earth shall be full of the knowledge of the Lord, as the waters cover the sea.” (Isaiah 11:9.) Then every living soul on earth will belong to The Church of Jesus Christ of Latter-day Saints. (The Millennial Messiah, pp.651-652)
Eventually All Will Be Converted or Removed
They shall not hurt nor destroy in all my holy mountain: for the earth shall be full of the knowledge of the LORD, as the waters cover the sea.
Joseph Fielding Smith wrote:
The gospel will be taught far more intensely and with greater power during the millennium, until all the inhabitants of the earth shall embrace it. Satan shall be bound so that he cannot tempt any man. Should any man refuse to repent and accept the gospel under those conditions then he would be accursed. Through the revelations given to the prophets, we learn that during the reign of Jesus Christ for a thousand years eventually all people will embrace the truth.
Isaiah prophesied of the millennium as follows: “The wolf also shall dwell with the lamb, and the leopard shall lie down with the kid; and the calf and the young lion and the fatling together; and a little child shall lead them. And the cow and the bear shall feed; their young ones shall lie down together: and the lion shall eat straw like the ox. And the sucking child shall play on the hole of the asp, and the weaned child shall put his hand on the cockatrice’ den. They shall not hurt nor destroy in all my holy mountain: for the earth shall be full of the knowledge of the Lord, as the waters cover the sea.”
This chapter in Isaiah, Moroni quoted to the Prophet Joseph Smith and said to him it was about to be fulfilled. if the knowledge of the Lord covers the earth as the waters do the sea, then it must be universally received. Moreover, the promise of the Lord through Jeremiah is that it will no longer be necessary for anyone to teach his neighbor, “saying, Know the Lord: for they shall all know me, from the least of them unto the greatest of them, saith the Lord.” (Doctrines of Salvation, 3:64)
Therefore, when the great day of the Lord shall come, the wicked who have merited banishment from a righteous government will be consumed, or the privilege of continuance on the earth will be denied. Therefore, according to the justice of the Lord, all who have not violated the right to remain will not be consumed. We are informed that these, although they may not be members of the Church, who are entitled to the blessings of the terrestrial kingdom, will be spared. Therefore, there will be millions of people on the earth during the millennium who have not received the gospel. Missionary work will continue with greater vigor and power than at any other time. This work must go on until all who are on the earth are either converted or are taken away by death. (Answers to Gospel Questions, Volume 2, p.200).
When that time shall come, the “earth shall be full of the knowledge of the Lord, as the waters cover the sea.” Wickedness shall be destroyed, for with righteousness shall Jehovah “judge the poor, and reprove with equity for the meek of the earth: and he shall smite the earth with the rod of his mouth, and with the breath of his lips shall he slay the wicked.” In that day there shall be no “divided Christianity.” All who will not repent and receive the gospel shall soon be removed, and they who shall remain shall learn to worship the true and living God in spirit and in truth. The Church of Jesus Christ shall have sway over all the earth, for Christ shall be the King and Deliverer. Peace shall prevail both among men and among beasts. Satan shall be bound and his dominion, which he has held by usurpation and fraud since the beginning of the earth’s temporal existence, shall come to an end. The rightful King shall reign and his saints shall possess the kingdom according to the vision of Daniel. (Doctrines of Salvation, 1:168-169)