Well I guess if you are a deaf person you should not ride a bike! And I guess a blind person would be good to go.
Vision is the absolute most important "sense" to use on a bike. Like it has been stated by one of the no music proponents the noise from wind and other sounds really distorts what you here- even the sounds of cars coming from behind. Use rear view mirror to see what is coming. Looking over ones shoulder can be dangerous, by doing so you are not looking at where you are going and secondly you can lose a bit of balance. Scan mirror every few seconds depending on speed of traffic.
Use a playlist so you do not have to figure out what you want to here. If you want to change the playlist do it safely when at a stop light/ sign where ever and don't try to do it while riding. I like using Bluetooth ear buds, no dangling wire to get stuck.
Some people are challenged when it come to "multi tasking", I understand and I mean them no disrespect. But, if you can use a rear view mirror and you can stay focused while listening to music there is absolutely nothing unsafe about it while riding a bicycle.