The rule is simple: The driver chooses. They're doing the work; they focus on the road and keep the passengers safe and happy without getting lost. The driver can't take in the scenery and relax the way the shotgun side can. Of course, there are limits. Playing the same song on endless repeat is a recipe for disaster. And if you're driving a car full of nuns, maybe hold off on blasting Black Sabbath. Unless they're into Ozzy. We don't judge. Anyhow, extreme circumstances aside, the driver says what's up when it comes to music, period. It's only fair.
The co-pilot covers the navigation, the snack distribution, and keeping the driver alert and engaged through a long haul. It follows, then, that the passenger should control the radio. The driver is preoccupied anyhow, and it's the passengers who fully pay attention to the sounds. A really great co-pilot makes playlists ahead of time so that everyone in the car will enjoy. The driver is already doing enough. This is for their own good.
The responsibilities of the shotgun rider are almost equally as important as the driver's, as he/she is in charge of how enjoyable the road trip will be. Long road trips are not ideal situations for the driver to be in charge of the music, so the shotgun rider must rise to the occasion. Whoever is occupying shotgun must keep the music selection enjoyable at all times.