Below is a video made by my wife that shows what happens to her in-car entertainment system when her iPhone 7 Plus is connected to it via Bluetooth. The problem is not with iOS 10 as she experimented with connecting her iPhone 6S Plus which also has iOS 10 installed.
I just saw today that BMW owners are having similar issues. Hopefully this is a simple software fix that Apple can push to users and not something that needs to be fixed on the automaker’s side. If that’s the case I fear the problem will be ongoing for quite some time.
Here are some other links describing the problem others are having.
https://www.neowin.net/news/some-iphone-7-owners-are-facing-bluetooth-issues-with-their-bmws
http://gizmodo.com/the-iphone-7s-bluetooth-is-totally-screwed-up-for-some-1787276957
http://www.macrumors.com/2016/09/29/iphone-7-bmw-bluetooth-audio-issues/