Recently, Google updated their permissions requirements for all apps. To ensure the game app has access to log you in with your different Google accounts, please follow the steps below.

Switch between multiple Play Games profiles

If the quick profile switcher is turned on in a game, you can:

1. Long press on the game icon.
2. Select Choose profile.
   • This option will only appear when multiple Google Accounts are present on the device.
3. Choose from one of the options listed.
4. Tap Save.
   • The game will start with the selected option.

Switch between multiple Play Games profiles with Android settings

1. On your Android phone, tap Settings  > Google.
2. Tap All services.
3. Scroll down until you see Settings for Google apps > tap Play Games > Sign in account.
   • To change default profile for games:
     1. Under the “Change the default account for games” section, tap Change.
     2. Tap on one of the 3 options provided.
     3. Select a profile.
        • Your changes will auto save.
     4. At the bottom of your screen, you’ll find a confirmation pop-up.
   • To change profile used for a specific game:
     1. In the “Change the account by game” section, scroll to the game.
     2. Next to the game, tap Change.
     3. Select a profile.
     4. Tap Save.
     5. When the action is complete, at the bottom of your screen, you’ll find a confirmation.

Official documentation from Google: How to switch Play Games profiles on mobile