Is this asbuilt data from the 4" Sync or other? It is mostly ok but the vehicle data in 7D0-05-xx thru 7D0-07-xx need to match your vehicle or the nav will not work properly.
I know it os a pain but did you do a master reset after you did the change and delete the car Bluetooth from the phone and then re-pair the Bluetooth connection?
Also can you post a Pic of your about Sync screen so we can see the version information of the software on your Sync unit? You can redact any information you care about.
Just to verify you have tried both Apple and Android phones and had the same problem.
If that is the case, then it seems that there is a problem with the software on your unit in dealing with phine calls as you had verified that Bluetooth works for all other Bluetooth related functions. The only thing left to try is to update the Sync in your unit and see if that resolves it. Or if you bought a kit to do this, go back to where you bought the kit from and ask them for help.
Based on the VIN asbuilt info you did not have a 7D0 asbuilt. You need the asbuilt from a comparable 2016 Mustang with Sync 3.
This is the OEM Sync 1 in your vehicle…
7D0
F110>DSE1BT-14D212-AE
F111>FR3T-14F130-BB
F113>FR3T-14D212-FD
F141>ET341699
F188>E1BT-14D205-AEnd the ‘APIM’ was
FR3T-14D212-FD is a Sync 1 unit. You would need to use a prewired kit for adapting Sync 3 to your vehicle. Or rewire yourself. This is a wiring chart to help.