Even if I thought it was completely safe, which I doubt it is, I wouldn't want to listen to music on a ride. I quite enjoy the sound of the bike; if I get bored on a solo ride, I just start talking to myself.
In Chicago I used to see wankers riding along with earbuds in, both hands texting on their smartphone (look ma, no hands!) not paying attention to anything around them. These are the same people who blow red lights and don't even want to yield to pedestrians in the crosswalk. They get killed every now and then. Perhaps that put me off to music while cycling, plus every group ride I've ever been on prohibited earbuds. Another reason is that I care about audio quality, so I don't do low volume or only one earbud in. That would drive me nuts. If it's worth listening to, it's worth listening to with good quality sound, and actually paying attention to the music. If you feel comfortable sharing the road with cars and pedestrians while listening to your music, good for you. I don't. Please be careful out there.
Running is another matter. It's quite boring to me, compared to cycling, and I don't run in traffic, so I'll invariably listen to music then. The same goes for indoor cycling training or lifting weights. I usually go with metal/hard rock or some heavy EDM. If I am deliberately trying to keep the pace slow on an easy day, I'll pick some more chill music. Alternatively it can be fun to shuffle a playlist with fast and slow tempos, and turn it into a random interval workout.
Almost forgot, riding with headphones is a Rule #62 violation. I might have to try out some of those bone conduction headphones, though...