Well, what kind of consistency do you have? For example, what do you say to LDS Mormons who may claim that fLDS Mormons are not true Mormons? (Is it unkind, unnecessary and un-'Mormon' for such distinctions to be made?)
This is not quite the same comparison.
The Church of Jesus Christ of Latter-day Saints IS a specific organization. Christian does NOT denote a specific organization.
Fundamentalist Mormons do not want to be known as Mormons. They want to be knows as a break away or protestants of the Church of Jesus Christ of Latter-day Saints. The biggest issue being they want to live Polygamy.
Currently, a polygamist is immediately excommunicated from the Mormon Church.