I know a lot more can be said about this, but here's an answer I wrote awhile back!
Why and when did Westerners stop to refer Muslims as Mohammedans?
Short answer, as I summarized in the previous question, "when people started thinking of Islam as a valid religion and not just an antithesis of Christianity", which was in the 16th century at the earliest, and in the 1970s (!!!) at the latest.