Discovered on Ubuntu 20.04, kernel 5.4.0-33-generic. Not tested elsewhere, but reproducible every time on my machine for final versions back to 1.13.2.

Exact steps to recreate:

1. Select desired audio output in Settings > Sound > Output Device
2. Start Minecraft
3. Confirm that buttons and music play through that audio device
4. While the game is still running, change Settings > Sound > Output Device to an alternative one
5. Confirm Minecraft is still playing audio through the first device

Let me know if it's just my machine, or if there really is something funky going on somewhere.