Change Destiny Activity & Progression to checked on the website not the app. Clear your cache and revalidate your login. If needed select the logout everywhere function and clear your cookies. Happened to me once and it just wouldn't acknowledge it until I did all this clearing.
It can take a while for third-party apps to catch the change, check it again after an hour or so.
One thing to do in the meanwhile is double check that both settings are enabled, as your game history is still hidden on Bungie.net too.
[quote]Show my Destiny game Activity Feed on Bungie.net
Show my Progression - what I've completed in Destiny and my current status[/quote]