Beastie Boys came out earlyish, in the Run DMC days, before rap would transition to what it would become later.
As far as appropriation? Look at Vanilla Ice v Eminem.
The Beastie Boys and Vanilla Ice are more contemporary to each other than Vanilla Ice and Eminem. The Beastie Boys first album came out in 1986, and Vanilla Ice's first album came out in 1989, while Eminem's first album came out in 1996.
Of course there was no such thing as 'cultural appropriation' back then, just like there was no such thing as 'cultural appropriation' when Elvis played Rock 'n Roll inspired by black performers in the 1950's, and The Yardbirds played the Blues in the 1960's. All of those people performed the music because they enjoyed listening to it. Plenty of people criticized Elvis, but most of that came from whites who thought the music was beneath white people to perform. Plenty of Blues performers criticized the Yardbirds performances because the Blues just wasn't the Blues if it wan't performed by black artists.
The critics were all wrong, and all of those artists that were criticized became successful despite the criticism. Why anyone would want to guard their culture, whether it be in the form of music, or story telling, or hair styles, from being more widely disseminated is beyond me. If you enjoy that culture, why wouldn't you want more people to also receive enjoyment from it? That is what makes the idea of 'cultural appropriation' incoherent to me. Culture spreads beyond the originating group because people outside that group enjoy it, so why deprive others of something you also enjoy?