What "fundamentalist" beliefs are most commonly rejected by "moderate" Christians? On this site there is plenty of information about what the "official" doctrines of various denominations are, but I doubt that the majority of Christians follow all of these to the letter.

Have there been any studies done to identify beliefs taught by a denomination, but which are widely ignored or not given much weight by its members?

An example would be self-identifying Catholics who use contraception.

To avoid the "no true scotsman" fallacy, consider a member of a denomination to be anyone who identifies themselves as such. 

I'm mostly interested in protestant views, but interesting examples from other groups are also welcome.
The hardest part in this answer is to distinguish Evangelicals from Fundamentalists, who share the same doctrines, but a different culture. 

The Fundamentalist movement itself takes it's name from a set of books called "The Fundamentals," published in 1925 as a reaction to modern liberalism in church polity. It basically called for a return to literal interpretation of the Bible and an increased focus on holiness. After the humiliating press from William Jennings Bryan in the Scopes Monkey Trial in the same year, the movement also advocated a complete separation from and rejection of the culture. This has the practical result of demphasizing missions in most truly fundamentalist churches. 

In the 1950s, Carl Henry, Billy Graham, and others reacted to this gap by telling fundamentalists they needed to reenage the culture- the foundation of evangelicalism. And, with Roe v Wade in the 1970s most remaining fundamentalists came to believe that engagement in politics was necessary. 

Since Fundamemtalism itself is a movement and not a denomination, it is not possible to speak of doctrines or polity (though in effect most are Baptists in these matters) but rather culture and emphasis. 

Primary distinctives are thus Literal Interpretation of the Bible, a rejection of theologically liberal learning (especially of the late 1800s) and a call to be separate from the culture.