If Mormons believe the LDS Church is the only true church on earth, does that mean they think they are the only true Christians?
Mormons do believe the LDS Church is the only church on earth with the priesthood, or the authority of God, which is necessary for the “legal” administration of ordinances like baptism and the sacrament. But Mormons do not believe that being a follower of Christ means you have to be a Mormon, and for Mormons, the only requirement to be a Christian is to believe in Christ and try to do what he taught. This is why Mormons refer to any religion or church based on following Christ as a Christian religion.
Mormons believe that being a Mormon is no guarantee of salvation, and that not being a Mormon is no guarantee of damnation. We believe there are untold millions of non-Mormons who will be saved in Heaven, and there will probably be a fair number of Mormons who will not be if they don’t live up to the tenets of their religion.