Hello kdeemer.
Welcome to Apple Support Communities. I understand that 2017 Subaru Outlook and Bluetooth audio starts playing as soon as the car starts. If you listens to part of a Podcast and leave the car, the Podcast will start playing when he starts the car even when the Podcast has been stopped and the app closed. You also mentioned that at other times music will play when the music app isn’t open. I’m happy to help.
Let’s start by restarting your iPhone using the steps here: Restart your iPhone, iPad, or iPod touch - Apple Support After your iPhone has fully restarted, please see if this still happens when you start your car.
I also recommend that you’re using the latest software update. Apple has recently released iOS 13.1.1. If you haven’t already, please back up your phone and install the update using the steps here: Update your iPhone, iPad, or iPod touch - Apple Support
If updating to the latest iOS version doesn’t resolve this, please unpair your iPhone from your car radio and pair it again. Please check your car manual on how to do this.
Also, check the car manual to determine if the radio firmware is up-to-date.
Take care.