I listen to music while riding... solo. (The one time a week I ride with someone else I don't listen to music.) I'm either listening to '80s pop or 70s funk.
Riding hasn't changed what I listen to.
When I started running I wouldn't listen to music while running because I didn't want to ruin the simplicity of Running. All you need is a good pair of running shoes and a pair of running shorts.
Unlike running, cycling takes a lot more effort. Besides shoes and shorts you need hi viz shirt, Lube chain, inflate tires, helmet, fill water bottles, turn on blinky... so adding ear buds for music isn't much of a distraction for me.
Of course if I was forced to be on a MUP for training I wouldn't wear one but then again I wouldn't live somewhere I was forced to ride on a MUP.