I have a similar problem in a 2011 Ford expedition with the latest system I am map update 9.0x and the iPhone 7 Plus with iOS 10.1.1. The phone is able to connect via Bluetooth to the navigation system but the moment that any media audio is attempted to be streamed via Bluetooth, the system instantly disconnects. We have duplicated the issue with my spouse's iPhone 7 Plus. We have troubleshooted the issue with Ford sync tech-support and they couldn't figure it out. This system worked with our prior iPhones-a 5s running iOS 10.1 and a 6+ running iOS 10.1.1, with no issues.
iPhone 7 running iOS 10 point anything have major Bluetooth compatibility issues across car manufactures apparently. Please note that this appears specifically related to media streaming. Phone use including downloading the phonebook and contact list into Ford sync with navigation and voice command have no issues, which tells me that the connection will transfer data,