The LDS church teaches that their organization is a restoration of the original church of the apostles, as it existed in the 1st Century CE.  They believe that, when the last apostle died, the original Christian movement went astray, and eventually split into many different denominations which have rejected much of Jesus' teachings and are thus heretical. All of the tens of thousands of other Christian denominations are thus in error.

Many other Christian faith groups teach the opposite of this belief: that most Protestant denominations follow a common Christian tradition which is traceable back to the earliest days of the church. As Jude 1:3 says, non-Mormon Christians possess "... the faith which was once delivered unto the saints." It is the Mormons who have deviated from that tradition, and are thus heretical.

Many historians and liberal theologians suggest that both are wrong: that the beliefs and practices of the original Christian movement, the Jewish Christians, were quite different both from the Mormons and from other contemporary Christian denominations. By the second century CE, there were many "Christianities" in existence, all teaching different belief systems. There may have been more difference among those early forms of Christianity than there is between the LDS and Evangelical denominations today.
Friction between Mormons and other other Christians has been present during the entire history of the LDS Church. There were a number of reasons why most Christians rejected the Mormon movement during the 19th century:

1.Their religious exclusivity, communal lifestyle, and "Mormons first and for themselves" lifestyle were criticized.

2.Joseph Smith's visions were rejected as frauds.

3.Some of his theological teachings about the nature of God, structure of Heaven, requirements for salvation, history of the Americas, etc. were rejected as heresy.

4.Plural marriage in particular was considered totally unacceptable behavior by most non-Mormons.

5.Smith's elevation of three writings to equality with the Bible was considered deeply offensive.

6.Smith's new translation of the Bible was viewed as heretical.

7.Smith's political goals were viewed as threatening to his neighbors. They feared that he wanted to establish a theocracy.

The movement has been growing rapidly -- on the order of 10% per decade -- since it was founded. This is perceived by some Christian groups as a threat.

Today, even though plural marriage has been at least temporarily suspended in principle for over a century and in practice for almost a century, many of the above points of conflict continue. During the early years, opposition by other Christians was violent. Much blood was shed. Now, the battle it is a mainly war of words:

http://www.religioustolerance.org/lds_crit.htm