By default, your Church's contacts will have the option to be included in the frontend directory. If you want to, you can override this option in the admin area.
Within your ChurchBox instance's Admin area, click on 'Settings'
And then 'Advanced'
On the 'Advanced Settings' page, click on the 'Security Settings' tab.
Select 'Yes' from the 'Disallow Contacts opting in to the directory' dropdown and click 'Save'
Now your contacts will no longer have the option to opt in to the frontend Church directory and they will no longer appear in it.