First of all it depends on what type of music. I don't mind driving without it, as long there are sound effects I'm good to go. The answer to your question, music is not that important for me while playing a racing game.
I enjoy online interactive games. I told myself I would finish GTA 4 before moving into the 5 but I haven't played any games recently, too busy with a popular MOBA game.
Grant Theft Auto for me. I see a few of you are sharing the same sentiment. The reason I can't finish is because I can't complete some Missions. Its just sitting there in my computer taking up space.