Are you using iTunes Match?
I've never used the Music app, had to search to even find it. Not sure how one turns it ON/OFF as I don't see any controls for it except in Settings. And even there, I don't see any way to stop it. I'd suggest checking the controls you have in your car, also.
I said I've never used the Music app but I now remember trying to edit the list of "Featured Stations" in the past few months. Apparently that's not possible. Apple provides the list. Period. I can create my own 'stations' but the Featured list is hard-wired.
Oh well, I suppose I'm just not normal. (That's a surprise to anyone?) I think a car is one of the worst places I can think of to listen to music. Too much going on around me (often called traffic), too much noise (even in my new very quiet car), too many 'distractions' if I'm going cross country (anyone for scenery?).
So, I generally have BBC Radio or NPR news/talk shows (and with SeriousXM, NPR Talk). "Music" would occur during Prairie Home Companion! And very occasionally on Car Talk!