What exactly is an atheist fundamentalist? Define that for me. Because fundamentalism is defined as a "strict or literal adherence to a set of principals."
If that's all there is to it, then why do atheists oppose it?
The name 'fundamentalist' comes from a set of religious tracts published in Los Angeles in 1910-15, entitled 'The Fundamentals', setting out what the authors took to be the fundamental principles of Biblical Christianity, which the authors feared were being swept aside and dismissed by more avant-garde Christians.
Then the use of the word kind of broadened out over the years, coming to refer to the wing of (usually Protestant) Christianity that held tightly to such fundamental ideas as Biblical literalism and inerrancy, belief in Christ's miracles and physical resurrection, justification by faith, the physical second coming, and literal heaven and hell. The word was already turning into what some philosophers call a 'family-resemblance concept', since fundamentalists didn't neccessarily share belief in the same exact same list of fundamentals, but they agreed on enough of them to have a family resemblance to each other that justified use of the same word to refer to them.
(Human cognition often works by association, so family resemblance concepts are very common in our language and thought.)
Gradually, the use of the word expanded further, to embrace religious expressions in other religions that resembled the Protestant traditionalists in what were perceived to be significant ways. There are obviously Muslims, perhaps the majority in some places, who are Quranic literalists, place great emphasis on strict adherence to Shariah law, and so on.
And in yet another broadening of the term, the word 'fundamentalist' has come to be associated with some some broader psychological similarities that fundamentalists often seem to share in common and the word has taken on a more perjorative tone.
There's typically a very strong insider-outsider distinction. The world is divided into Christians and non-Christians. (Or whatever the distinction is.) There are often strong negative judgements projected at the outsiders. There is a kind of psychological grandiosity, an unshakeable belief that the chosen ones have access to unique and absolute Truth. There's a drive to proselytize, to convert the heathen, and to remake the rest of society in the image of their faith. These are people who think about religion much of the time, feel very strongly about it, and hence aren't exactly secularized individuals.
My point has been that a certain kind of atheist spends a great deal of time thinking about religion and cares very passionately about it. They can have their own style of grandiosity, often believing that they are more intelligent than other people and that they possess the one saving Truth of reason and science. They dream of the day when religion, with all of its intellectual obscurantism and moral evil, is swept off the Earth entirely and forgotten.
Even in matters of smaller theological detail atheists sometimes resemble the religious fundamentalists. Some atheists study their Bibles for hours on end and quote Bible verses to illustrate whatever their anti-Christian point is. They read their Bibles with a fundamentalist-style literalism and stoutly reject the kind of allegorical and historical interpretations that many non-fundamentalist Christians favor. They are as opposed as any Christian fundamentalist to what both call "picking and choosing", selecting some Bible verses to believe and follow while dismissing others.
These kind of atheists are rarely aware of it, but there is a distinct and narrow Christian theology implicit in how they themselves perceive and interpret Christianity.