Journal of Discourses, Brigham Young 11:42

If the Latter-day Saints think, when the kingdom of God is established on the earth, that all the inhabitants of the earth will join the church called Latter-day Saints, they are egregiously mistaken. I presume there will be as many sects and parties then as now. Still, when the kingdom of God triumphs, every knee shall bow and every tongue confess that Jesus is the Christ, to the glory of the Father. Even the Jews will do it then; but will the Jews and Gentiles be obliged to belong to the Church of Jesus Christ of Latter-day Saints? No; not by any means. Jesus said to his disciples, “In my Father’s house are many mansions: were it not so, I would have told you. I go to prepare a place for you, that where I am, there ye may be also,” &c. There are mansions in sufficient numbers to suit the different classes of mankind, and a variety will always exist to all eternity, requiring a classification and an arrangement into societies and communities in the many mansions which are in the Lord’s house, and this will be so forever and ever. Then do not imagine that if the kingdom of God is established over the whole earth, that all the people will become Latter-day Saints. They will cease their persecutions against the Church of Jesus Christ, and they will be willing to acknowledge that the Lord is God, and that Jesus is the Savior of the world.

Journal of Discourses, Brigham Young 12:54

Now when Zion is built up and reigns, the question may arise with some, will all be Latter-day Saints? No. Will there be this variety of classes and faiths that we now behold? I do not know whether there will be as many, or whether there will be more. …. In the millennium men will have the privilege of being Presbyterians, Methodists or Infidels, 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.

Journal of Discourses, Brigham Young 2:47

Do you expect that every person will be destroyed from the face of the earth, but the Latter-day Saints? If you do, you will be mistaken. Many of our Elders labor under these erroneous expectations when reading over the sayings of the Apostles and Prophets in regard to the coming of the Son of Man. In one verse the Prophet will be describing the second Coming previous to the commencement of the Millennium, and perhaps in the same verse he will describe a scene that will take place after the Millennium, and when the earth will be cleansed from all wickedness, after Satan has been let loose a little season, and had another tour upon it, and after it is renovated and becomes sanctified, and is like a sea of glass, as John describes it. Will this be in the Millennium? No. But the order of society will be as it is when Christ comes to reign a thousand years; there will be every sort of sect and party, and every individual following what he supposes to be the best in religion, and in everything else, similar to what it is now. Will there be wickedness then as now? No. How will you make this appear? When Jesus comes to rule and reign King of Nations as he now does King of Saints, the veil of the covering will be taken from all nations, that all flesh may see his glory together, but that will not make them all Saints. Seeing the Lord does not make a man a Saint, seeing an Angel does not make a man a Saint by any means. A man may see the finger of the Lord, and not thereby become a Saint; the veil of the covering may be taken from before the nations, and all flesh see His glory together, and at the same time declare they will not serve Him.