As an Admin
To hide a member's contact information on the website and/or their directory profile, start by going to the record in the admin.
Then go to the Settings tab, and toggle the appropriate checkbox:
Hide on Website - this hides the entire record on the front-end
Hide Contact Information on Website - this will still show the record on the front-end but hide their contact information (Address, Phone, and Website)
Hide Address on Website - this hides only the address on the front-end
Allow Members to Set Their Preferences
Admins can also decide whether members can update their directory preferences themselves. To allow updating of member directory preferences on the Member Compass, admins will need to go to the Membership tab of Association Settings.
Then check the box for Allow users to adjust their privacy settings.
This will give the same privacy options admins see on the Settings tab of a record to all users at the bottom of their Profile settings in the Member Compass.