Just use signed MOD and follow the tutorial
1. Download Brown Dust 2 from google play
2. Login with google account
3. Immediately quit the game after login
4. Open file explorer app and search for com.neowizgames.game.browndust2 (located in OBB folder)
5. Rename it to any or move it to somewhere else (to prevent the folder being deleted- step 6)
6. Now delete/remove the Brown Dust 2
7. Install Brow Dust 2 mod (signed one) but do not run it yet !
8. Go back to file explorer app, move/rename back the folder to com.neowizgames.game.browndust2 into OBB folder
9. DONE ! Run the mod and you should able to login google account
I use signed mod and its work for me to google login