In Christianity, "Fundamentalist" refers specifically to a Protestant/Evangelical movement that was named for a series of essays published before and during WWI, which outline certain specific doctrinal positions. The movement arose largely in response to opposing beliefs which themselves date to the mid-late 1800s. Being "unwilling to budge" might make someone a literalist or a dogmatist, but being a Fundamentalist is more specific.

Among Americans who call themselves Christian, few are anything close to true Fundamentalists [0]. Most are hybrids whose beliefs have been assembled in bits and pieces from pastors, books, etc. which includes some fundamentalist-inspired ideas, some ideas that resemble fundamentalist ideas but are actually much older, and some ideas that are completely opposite of fundamentalist ideas. People whose beliefs are mostly Fundamentalist are a very small subset of Christianity, both globally and in the US.

[0] note that "no true Scotsman" is only a fallacy if one is using inappropriate criteria to determine group inclusion/exclusion. It's not a fallacy to point out that James Doohan wasn't really Scottish.