To me, stress should correlate positively with code quality. I've met too many developers in my life that work away while listening to music from their headphones, doing a low-stress job of copying and pasting code around without the least concern for structure or maintainability. I curse and sigh all day long, but at least I try to write code that looks and behaves as I think it should, not just whatever works.
What? Copy and pasting code is not correlated with wearing headphones. The music is there to keep me focused (and to help block out open plan office noise).
I curse, too - although more quietly now everyone can hear.
Most probably it's just how my brain is wired - contrary to a lot of people, I just can't listen to music and concentrate on something different at the same time. So the idea of someone coding while listening to music makes me instinctively think they're not dedicating 100% of their brain to what they're doing. But I understand that this doesn't apply to everybody.
I have this problem too. However, being in an open-plan office, I have to choose the lesser of two evils: monotonous music vs human voices. I find the latter very distracting. I can even go to sleep with music playing but never with people talking around me. Of course given the circumstances, you could probably guess that I pick instrumental music and mainly music without strong 'movements' (I don't know the right term).
Eventually, I felt that listening to music on headphones everyday for many hours is going to affect my hearing on the long term and I decided to sacrifice productivity to keep my (better than average) hearing in good condition.
I may be rambling a bit but the point I am trying to make is that people are different and also in differing circumstances. So, is possible that you will choose likewise if you were in their place (and were of similar constitution).
I use music in order to support my development task: The playlist sets the mood like a good movie score, so the choice of music can depend on how focused and fast-paced my task is.