Getting better results with the Subaru Infotainment unit and Android Auto and Bluetooth. Still have the radio start with the car start minor nuisance but with the volume knob run down to zero at least you don't have to hear it. Audio for phone calls is independent and that's a nice touch.
If you are having Android phone connection issues also, something to try is re-booting your phone in "Safe Mode" - yes, shades of Microsoft Past!!! Not an Android expert here but it apparently will start up your phone with all the add-ons from the Google Store deactivated temporarily. The phone is a hand-me-down Nexus 6 that is almost as big at the Impreza 6.5" screen itself!!!! Hey, it was free.
When I did this the Bluetooth connections for both of my cars, Subaru and Mazda, became reliable and with the "phone audio" option checked every time. That told me that some gremlins were involved with my downloaded installs on the phone. Android Auto is ghosted out here, as it was a downloaded app. You can test your Bluetooth issues this way.
Went to church, lit a candle, came home and began the uninstall, reinstall, test, repeat ... until I believe I now have the thing reasonably stable for a few days now. Didn't want to wipe the thing as I have stuff on it that I don't want to lose. My major suspect is now Android Wear which tries to work with your Android Watch - also a free item, found under the Christmas tree. If you haven't guessed yet, I'm family with some Google employees. I think I'm going to suggest a new app to them - Android Referee or maybe Android Nanny or how about "Android Prefect of Discipline".