My issue is similar, but not the same. My BMW will only allow me to make calls via bluetooth now, not receive them. I've had multiple issues across 4 different bluetooth devices since this upgrade. Judging by the Android forums, this is a known-issue and is resolved in 7.1.1, which is sadly not available for my HTC ONE M9 at this time.
I'm on Note 5, SM-N920T. Have never rooted, use relatively limited quantity apps, mainly Pandora, light browsing, and basic Google functions.
I am posting this to a couple different post-Nougat upgrade issues, because this fixed two of my major problems. I tried wiping cache partition, and now missed calls don't prevent me from placing outgoing calls after anymore and the Bluetooth is back to normal functionality. I don't know why this fixed things for me and I can't prove that it is the real solution in the end, but may be worth a try if it happens to you too.
1. Turn off and shut down phone completely.
2. Hold Volume UP + HOME + Power all together until it boots to a light blue screen and says "Installing system update"
3. Let go of buttons and wait, it will say "No command" with a dead android looking icon... don't panic, just continue waiting and in about 10 seconds it takes you to the Default Android Recovery.
4. Navigate, using Volume up/down keys to the "Wipe Cache Partition" and press the power button.
5. Then select "yes" again with volume and power button to confirm.
6. Then just select "Reboot" with power key again.
Good luck, and I hope this helps.