I don't often play music while riding, but do sometimes listen to audio books. I also play music in my head and often sing while riding. When I do play music it is a pretty eclectic collection John Prine, Avett Brothers, Jimmy Buffet, Simon and Garfunkel, Norah Jones, Guy Clark, Jimmy Hendrix, Stevie Nicks, Van Morrison, Willie Nelson, Woods Brothers, Ben Sollee...
I always found I could hear the ambient sounds fine when i wore my earbuds. I trail ran with them and was never surprised by faster runners or mountain bikers overtaking me. I could hear where my dog was without looking.
I generally found that paying attention was the bigger limiting factor. When I used to trail run I ran into many people on the trail who despite my intentionally making a lot of noise when overtaking them would jump out of their skin when I passed them. It seemed impossible to warn them without frightening them since they were oblivious enough that they didn't hear anything that didn't startle them. These were folks without earbuds. They were just totally zoned out. I never really understood because it was uusually in an area where you generally knew where everyone within a quarter mile of you was if paying attention at all.
I get the same thing when trail riding, but I understand that more since the approach is faster and quieter. I think there is the same danger on the road and it is easier to get zoned out cranking out long miles. I like to get totally absorbed in the riding, but I make it a point to keep my ears engaged. I don't find that my ear buds hamper that. Some designs may be worse than others though.