If opening a door, while exiting, ordinarily shuts off the radio and that feature has stopped working, I’d be taking a look at the door latch switch located with the door latch on the door’s end (opposite end from the hinged end). It should be a plastic piece that moves (integral) with the latch itself. Those switches sometimes begin to stick.
With the door open and radio playing, try gently moving the switch piece and see if you can make the radio stop. If so you could see about a latch/switch replacement, but first I’d try spraying the latch with a silicone lubricant as I’ve seen GM technicians recommend. Use eye protection and be sure to use the tube supplied with the spray can to direct the spray at the switch. Opening and closing the door several/many times should help work the silicone in where it needs to go.