I don't know Islam enough to speak about it when it comes to this type of distinction. LDS however, worship Jesus, and God the Father. The modern prophets are there only to clarify doctrine, perform ordinances, and help direct the members toward Jesus. They don't supercede Jesus.
This whole thing really just depends on the definition you come up with. You could write a definition that Catholicism is the only Christian religion, because it is the direct decendant of the church Christ built. All other worshipers are offshoots. In practice, that isn't a great definition, because Catholicism isn't close to a majority of people that worship Christ. So you need to expand to include those offshoot religions. You don't want to go too far though, otherwise you get people making their own Christian church, but doing whatever they want in the name of it.
So it is all pedantic talk. I think LDS should be included in Christianity, but I can understand why someone would argue against it, in the name of trying to keep to the core Christian religions.