History must be replete with situations such as where a music producer buys a song outright from a semiliterate performer for 50 bucks and then turns it into a million selling hit with no royalties for the original writer. And that type of exploitation has historically been enabled or facilitated by a classist or racist framework where the original writer would have no conceivable access to fair compensation nor to proper legal representation. And that is certainly appropriation. But the fact that it's cross-cultural may be relevant to the appeal of the stolen good, but it's incidental to the act of thievery.

Hence, if Sting stole musical licks from specific performer(s), that's a problem. If those people would've been entitled to compensation but for the fact that they were poor island countryfolk incognizant of their rights, that's a problem. But if he just borrowed his musical aesthetic from reggae or from "Jamaican culture," that seems morally uncontroversial to me. Maybe musically derivative, but that's a matter of taste.