I had the same problem at work with colleagues playing radio all day. I found it very hard to concentrate on what I was supposed to be doing, especially as my job involves listening. The noise of the office and the radio as well as phones was a nightmare and for 6 months we also had demolition work outside! It got to the point where I found it hard to sleep, with lyrics and songs constantly going through my head, and it was music I hated. At one point I seriously considered taking a screwdriver to it or smashing it up when nobody was around! I mostly listen to chilled, downtempo music, but I don't mind loud or agressive music like metal or drum and bass as long as it is good. Chart music on the other hand is just shrill and annoying with 4 note melodies repeating over and over that make me feel really angry.
Well we nearly had a fire in one of the offices and after that the managers wanted to know every electrical item in each office, that's when they said we weren't really supposed to have radios. But nobody took much notice. Finally I found a notice on the intranet saying that radios were not allowed as they wouldn't pay for licencing, I showed that to the manager and told them it was distracting me and she was very understanding and now there are no radios! Perhaps you should look up if there is a policy at your workplace regarding radios and show it to your boss and let them decide, in the UK you have to have a licence now for playing music (a big brother policy to be sure - don't know if the US has this?) but you could look into whether your workplace has paid for one and if not casually mention it to your boss, and as there could be fines they will be sure to take action. I would try to avoid direct conflict as some people get really annoyed if they cannot listen to their awful music, yet they impose it on others without a second thought.