The nature of God, like the nature of mammals, is what defines God. The Christian God has a certain nature; there are essential attributes that make the God of Christianity God. If one teaches that God has different attributes, you are no longer talking about the God of Christianity and therefore you no longer teaching Christianity. You are teaching something fundamentally different.
In my last two posts, I've begun to explain some identifying characteristics of any religious movement that could be defined as a cult of Christianity. While the word cult immediately evokes mind control or armed compounds, it's more formal definition much more broad. As I've explained before, the word is used to express the idea of being seduced away from the historic Christian faith. That is really the third marker of cult of Christianity: it is any sect that claims to be Christian but teaches a denial of one or more of the essential doctrines that make Christianity what it is.
What are some of the essential doctrines of Christianity? Well here are a few:
- The nature of God: Christianity defines God as one being in three persons. Jehovah's Witnesses teach that God is one person and Mormons claim that God is multiple beings. Christian Science also denies the Trinity, with Eddy writing "The theory of three persons in one God (that is, a personal Trinity or Tri-unity) suggests polytheism, rather than the one ever-present I AM."
- The nature of Christ: Jehovah's Witnesses deny the deity of Jesus, claiming He's a created being. Mormons hold that Jesus was the physical offspring of Elohim and a spirit brother of all humans. In Christian Science, "Jesus Christ is not God, as Jesus himself declared, but is the Son of God."
- The nature of salvation: Salvation is wholly accomplished by Christ on the cross. However the Book of Mormon teaches that "it is by grace that we are saved, after all we can do."  The Watchtower teaches that Jesus' death paid the ransom only for sin inherited from Adam, but believers' names won't be committed to the Book of Life until they pass the test of loyalty. Christian Science teaches ""One sacrifice, however great, is insufficient to pay the debt of sin. The atonement requires constant self-immolation on the sinner's part."
Heresy used to be a more serious charge as people understood that by changing any essential doctrine also changes the nature of the belief. It would be like claiming to be a fish but not having gills. For while these movements may look Christian on the outside, their nature shows they are not what they claim to be.
 Eddy, Ibid. 361. <http://christianscience.com/read-online/science-and-health/(chapter)/chapter-xi-some-objections-answered#anchor.1.11>
 Smith, Joseph, Jr. The Book of Mormon. Salt Lake City: The Church of Jesus Christ of Latter-day Saints, 1948. Print. 92.
 McClane, Joe. "Understanding the Jehovah's Witness Teaching of the Ransom Sacrifice and the Atonement." Accessed online at http://www.joemcclane.com/ROB/ransom.pdf> 8/2/2013
 Eddy, Ibid. 23. < http://christianscience.com/read-online/science-and-health/(chapter)/chapter-ii-atonement-and-eucharist#anchor.1.2 >