I also just got this bug and have not seen this anywhere else on the internet. i am on PS3 and i can't turn on the radio or hear any music in other cars, buildings(strip club etc).
I have completed the main game and was was doing side content; i was about to 100% the game when i kept reloading a quick save to do a stunt jump which then resulted in the music being halted.
I've tried switching characters, saving in the bed waiting for a day to pass, seeing if i could hear any music elsewhere, tried changing the radio through the radial menu, in the settings, and by just tapping left on d-pad, i even tried reloading an old save with no luck. This is the only bug i have encountered and if anyone has any suggestions it will be appreciated.