As a superuser, you can turn on or off the need for approval for changing the due dates on actions on a modular level.
To access this setting go to Menu -> Super -> Modules -> [Relevant module] -> Admin tab.
At the bottom of the page, you will find the toggle to turn this on or off.
With this setting turned on, any change to the due date will be sent to the action creator for approval. Any changes to the due date are automatically approved if it is off.