I'm not sure there is much correlation between the two, at least in my case.
I fall squarely into the "no music" camp, and have since I was a child where music during study would drive me crazy. Music while coding is just a distraction to me.
However, I really love F.lux/Redshift. One of the most relaxing and productive things for me is to work in a dim or dark room with the display shifted to a fairly low color temp. By contrast, during the day I prefer fairly high contrast, using the VividChalk theme in Vim. In the past I would switch to a lower contrast theme like OceanDeep, but never found one to work well with red hues yet, which I prefer in dim light (partially as a throwback to old amber monitors.)
As a side note, I will agree with everyone saying the automated time based shifts are annoying. I usually find myself pausing or disabling it. Having it triggered off ambient light levels is the logical way, imho.
I also prefer nobody throw hambmurgers at me while coding, but if they want to toss them onto the corner of my desk for later consumption, I won't complain...