Yes they can now
But, before 1978 the black people were only allowed to be bapitzed in the Mormon church and nothing eles.
Black Skin and the Seed of Cain
Brigham Young taught a much greater extreme. In a sermon given on March 8, 1863, Young stated, “Shall I tell you the law of God in regard to the African race? If the white man who belongs to the chosen seed mixes his blood with the seed of Cain, the penalty, under the law of God, is death on the spot. This will always be so” (Journal of Discourses, 10:110).
mrm.org/topics/miscellaneous/black-skin-and-seed-cain
third LDS President John Taylor And after the flood we are told that the curse that had been pronounced upon Cain was continued through Ham’s wife, Because it was necessary that the devil should have a representation upon the earth as well as God" (Journal of Discourses 22:304).
2 Nephi 9:15: “And it shall come to pass that when all men shall have passed from this first death unto life, insomuch as they have become immortal, they must appear before the judgment seat of the Holy One of Israel,…For the Lord God hath spoken it, and it is his eternal word, which cannot pass away, that they who are righteous shall be righteous still, and they who are filthy shall be filthy still; wherefore, they who are filthy…shall go away into everlasting fire, prepared for them; and their torment is as a lake of fire and brimstone, whose flame ascendeth up forever and ever and has no end.”
Men have the same talents and intelligence there, which they had in this life. They possess the same attitudes, inclinations, and feelings there which they had in this life" (Bruce R. McConkie, Mormon Doctrine, 2d ed., p.762)
One, there was no biblical reason for the discrimination in the first place; and two, there was no precedent according to Mormonism to lift it.
mrm.org/topics/miscellaneous/black-skin-and-seed-cain