From time to time, the topic of evolution comes up on the Bloggernacle. It seems that there are four possible views:
1 Young-earth creationists assert that the earth is approximately 6,000 years old and that all species were unchangeably created at the moment of origin by divine miracle.
2 Old-earth creationists reject natural selection as an explanation of biological species, but they do accept the age of the earth as established by scientific techniques such as radiometric dating. In this view, each "day" described in Genesis was a long time. The mechanism of creation is identical to the young-earth theory.
3 Theistic evolution is a common Christian view. In this view, evolution was the method of divine creation. This is the official position of the Catholic church, for example. I have also heard this position articulated by BYU biology professors who teach evolution.
4 Scientific evolution holds that all organisms come to be through entirely natural processes. In contrast to theistic evolution, scientific evolution holds that there is no design for living creatures and no necessary progression in evolutionary change, only adaptation to local circumstances.
I'm guessing that very conservative Mormons are young-earth creationists, that mainstream Mormons are old-earth creationists and that liberal Mormons believe in theistic evolution. I would guess that very few Mormons believe in scientific evolution (undirected adaptation). It would interesting to know what proportion of the LDS population falls into each of these buckets.
There's a strong association between creationist views and anti-gay sentiment. (People who hold one of these views tend to hold the other. Young-earth creationists, in particular, tend to be extremely anti-gay.) It's interesting that when creationism began its ascent in the U.S. in the 1920s, one of the main issues was race. Evolution was seen as justification for the mixing of races, which at the time was extremely controversial. Today, the issue is no longer race, but conservatives are anxious about the loss of strict gender roles and about homosexuality. A purely natural explanation of biological origins seems to intensify this anxiety.
Search YouTube for "Darwin's Legacy Stanford" for a series of useful lectures on evolution. Lecture 2 is especially relevant to the issue of religious views.