1920 in the religious sense (as is fundamentalism), from fundamental + -ist. Coined in American English to name a movement among Protestants c.1920-25 based on scriptural inerrancy, etc., and associated with William Jennings Bryan, among others.
Fundamentalist is said (by George McCready Price) to have been first used in print by Curtis Lee Laws (1868-1946), editor of "The Watchman Examiner," a Baptist newspaper. The movement may have roots in the Presbyterian General Assembly of 1910, which drew up a list of five defining qualities of "true believers" which other evangelicals published in a mass-circulation series of books called "The Fundamentals." A World's Christian Fundamentals Association was founded in 1918. The words reached widespread use in the wake of the contentious Northern Baptist Convention of 1922 in Indianapolis.
The original opposition to fundamentalist (within the denominations) was modernist.
Applied to other religions, especially Islam, since 1957.