Workaround…
Change your battlenet pwd via the Battle.net website. This will force a login screen on the Hearthstone app again, login with new pwd.
Play until you are ready to stop BUT before you quit playing, logout of your HS account (bottom right/switch account) then quit the Game.
Next start you will be promted for your login credentials, Login and play, then logout when done, login/logout until a fix is released.