The same thing happens with iPhone and car bluetooth. It is super annyoing and many times, a podcast will be playing in the background while the car has FM/radio selected. This is incredibly frustrating and bad user experience. The worst part is it is not clear if this is Apple's fault or some buggy old firmware in the car's audio stack that is at fault (this happens consistently on 2017 Tesla Model S).

I too have seen conflicts between CarPlay and the radio. My car's a Hyundai.

I mostly listen to the radio, with an occasional trip where I instead listen to a podcast or music via CarPlay.

What I've found greatly helps is when I finish a trip where I've used CarPlay after I park but before turning the car off I open my phone, open control center, tap the now playing widget, tap the symbol on that for output selection, and make sure it is set to iPhone Speaker. I then hit the Media button in the car and select FM. That starts the radio playing. Then I stop the radio and shut off the car.

Next time I use the car CarPlay connects normally but does NOT take over the media playback. If I hit the play button in the car it starts playing the radio.

This works fine for me because as I said I mostly listen to radio. It is not that big of a deal the once a week or so that I listen via CarPlay to do those extra steps at the end of a trip.

It would probably be a lot more annoying if I was frequently switching between radio and CarPlay.

In either case I would definitely like a setting somewhere that makes it so the play button in the car plays whatever source was playing the last time you turned off playback.