Xbox version 63.148795
Switching between party and game chat seems to have improved since the 9-25-2018 update however there is still a bug our party found. When switching from party to game chat by going through Xbox menu then pressing down on D pad the microphone icon shows in HUD and game chat seems to be working.

However, if you go back to party chat by using the Xbox menu while leaving the microphone icon on in the HUD and then try to switch back to game chat again through Xbox menu the game chat does not work. We tried this several times and got same result.

To fix this, we found out that when in game chat you must first turn off the microphone HUD icon by double pressing down on D pad before switching to party chat. Then switch to party chat. Then when you switch back to game chat you can turn on microphone with D pad and game chat will work. So you have to keep turning game chat microphone off before switching so it does not cause a problem.