If the term "fundamentalist" means anything other than "a person whom I hate", it should logically mean, and originally did mean, "a person who believes the fundamentals, the basics, of Protestantism or, by extension, who believes the fundamentals of any religion".

But a "fundamentalist" believes what they think are the fundamentals. If they think that Islam fundamentally forbids music, then it doesn't matter what you think or what twenty imams think are really and truly the fundamental aspects of Islam -- they are sticking to their fundamentals. Just like there are Christians who think hating homosexuals is one of the Christian fundamentals.