Just want to add a process/work-around I have discovered. This has worked the past couple of days though not perfectly. It isn't terrible, just an extra step and at least the phone/stereo connection works, better than nothing.
Step 1 - Quit music, podcast, etc apps. I use the native music app & downcast for podcasts. I quit out of both. (Haven't tested if having any apps open, maybe anything that uses phone speakers could interfere with car connection? Rampant speculation)
Step 2 - Plug into the car cable
Step 3 - The car should recognize the iPhone and launch your music, starting with whatever song comes first in the alphabet. (Some wonkiness if the cable connection isn't perfect, happens to me occasionally due to the 30-pin to lightning adapter, still 8 or 9 out of 10 times it seems to be working)
Step 4 - I can now choose what I want to hear. (The car stereo interface has access to playlists, artists, albums, etc. Or I can open Downcast and listen to podcasts. Or if you prefer to the car stereo interface, open Music app & choose what you want)
this is working maybe 9 times out of 10, ok so it's more annoying for short bursts of driving such as several errands in the local area but for my commute or future highway trips it is good enough to get the job done.