Brian Hales writes in the book, Mormon Fundamentalism (Orem, UT: Millennial Press, 2008):
In writing about Mormon fundamentalists, I am aware that they prefer to be called “fundamentalist Mormons.” In choosing the terms I use, I do not wish to convey my disrespect. Yet for me, a true “fundamentalist Mormon” would embrace the whole of the Church’s fundamental teachings, not just a specialized version of one or two principles, and the need for proper priesthood authority to perform valid ordinances, including baptism, would exclude freelance baptism (those performed without genuine authority) as a gateway to becoming “Mormons.” These two concerns limit my ability to refer to “Mormon fundamentalists” as “fundamentalist Mormons.” All major religions have “fundamentalist” factions attached to them, and the Mormon variety shares many parallels with their counterparts of other spiritual traditions. In that context, they easily qualify as “Mormon fundamentalists.”
– Brian C. Hales, May 2008
Though I am an outsider, this conversation is intriguing. Brian sounds like a “fundamentalist Mormon,” insisting on fundamentals. Am I wrong on this?
Find out more at his website, Mormon Fundamentalism.
Jesus in Idaho Falls 
When President Hinckley said there is not such thing as a Mormon Fundamentalist what he meant was that if someone is truly dedicated to the fundamentals of Mormonism, then following the prophet is one of those fundamentals, even if what the prophet declares is to stop practicing polygamy.
And why should anyone follow a “prophet,” in this case, the4th President of the LDS church, Woodruff, when
1. His 1890 revelation ending polygyny was addressed to WHOM IT MAY CONCERN (the only ‘revelation’ from God in all of Patriarchal Scripture so addressed);
2. It did NOT concern Woodruff very much, seeing that he continued to practice polygyny and continued to take ADDITIONAL wives after the 1890 “manifesto.”
Please.
LDS are apostates.
They’re not Mormons.
Mormon Fundamentalists are Mormons.
By theological definition.