Some additional information on the cause of this bug, how to reproduce the issue and a workaround until Blizzard resolves the issue.
The issue appears to be a result of the way that Blizzard treats bluetooth devices that have both inputs (microphones) and outputs (speakers). When you connect a device that has both input and outputs, it appears to switch the sound over to some type of “headset” mode that disables any noise cancelling and causes the audio to stutter profusely.
This issue can be reproduced by connecting any(?) (I have seen the problem with Bose QuietComfort 35 II and PowerBeats Wireless) bluetooth headset that includes both a microphone and speakers.
As a workaround until Blizzard looks into this issue, you can get your sound working by performing the following steps prior to launching Starcraft 2.
- Connect your Bluetooth headset
- Open System Preferences -> Sound
- On the Input tab, change the input device to the built-in microphone on your Mac.
- Launch Starcraft 2
This was tested on a Late 2016 MacBook Pro running Mojave 10.14.5.
From what I have seen, there are similar issues which occur in Windows caused by the same issue. While I do not have exact steps to follow for Windows, I would expect changing the Input device would produce similar results.