I don’t know about the book from 300 years ago, but the movie from 1975 seems like it would be a more modern reference. Learned scholars might refer to books that are hundreds of years old, but a movie released in many living people’s lifetime seems like it would have more of an impact on current usage.
The movie in question (Man Friday [1975]) starts with Robinson Crusoe walking along a beach on his personal stranded island, when he sees footprints. He is instantly elated at the thought of company or salvation, and goes running of to find the maker of the tracks. He comes along 4 black men, eating a 5th, cooked person (we know that they were all friends who got stranded, and in their custom, it is an honor to eat their fallen friend, who drowned). Crusoe quickly shoots 3 of the men, while the forth binds his own hands, to show he is no threat. Crusoe takes this man, at gunpoint, back to his home. Because he sees him as a savage, unfit to be given a proper name, he names him for the day of the week. He proceeds to use the man as a slave, even telling Friday that his name is Master, which Crusoe is called for the whole movie, except one scene. Friday himself breaks with Crusoe over the realization of what he is in Crusoe's eyes, and says he would rather die than live as a slave. He is referred to as a slave in one scene. Most communication is had while Friday has a gun pressed to his head or body, which he is told is imbued with White magic that only allows it to shoot black men.
Friday has his own perspective and agenda, but I think the important part is what Crusoe means in using the term "My man Friday". From Crusoe's perspective, Friday is an ignorant peon who he is tricking into doing his bidding so Crusoe can sit around reading all day, doing the "Master's work" of thinking. He tolerates Friday, but they are not meant to be equals. My man Friday seems to mean a slave, or at best, a lackey or errand-boy. I feel that this is a more correct interpretation of the phrase than "a person one can trust". As to whether it can mean a woman, that would be a "Gal Friday," but should have essentially the same meaning.
I wouldn't be surprised if the Cambridge or Oxford dictionaries went out of their way to avoid the "distasteful" subjects of slavery and prejudice, as many textbooks and reference materials have historically downplayed the importance and relevance of such topics.