I have CarPlay in my Toyota Aygo. I got the car last December, and CarPlay worked fine, until iOS 13. With the GM, the official release, and all three updates, it would crash. Other phones work fine in my car - my partner's, and two people at my Toyota dealership - but mine crashed CarPlay in a different Toyota.
So, after an hour to get through to a senior AppleCare advisor, he wanted me to set the phone up as new and see what happened. No crashes.
I was sitting in the car with nothing to do, so I signed into Apple Music. No crashes.
Then I signed into my Apple ID - which I didn't do during the initial setup - and it crashed. Signed out and back in again, twice, and it crashed each time. Signed in with a different Apple ID, no crashes.
So there's something in my iCloud data - which could be, what, contacts, calendars, phone call info, messages - that is corrupt and causing CarPlay to crash.
So, for anyone who is having intractable problems, try signing out of your iCloud account and see what happens. The support person I spoke to is going to escalate this, and hopefully there will be some resolution next week, but I wonder how they're going to solve this without nuking all my data (it might be possible to export everything then reimport it, but I don't think it's easy).