The 1Password 5.1 update seems to improve the situation with Touch ID. Most significantly, storing the master password in the iOS keychain seems to work now, whereas before I was often prompted to type the password.
The settings have been simplified. If you enable Touch ID, 1Password will always store the master password in the keychain; there is no longer an option to turn this off. If your iPhone supports Touch ID, you are no longer allowed to set a PIN code. There’s also one timeout instead of two, and there’s a new option to allow the use of third-party keyboards.