If you want to enable visibility controls in these web parts, you have to add the controls to the appropriate alternative forms and set the following properties of the web parts:
User public profile
•Form name - specifies the full name of the desired alternative form (cms.user.DisplayProfile by default).
•Apply visibility settings - check this to enable the visibility controls.
•Use visibility settings from form - can be used to select from which form visibility settings should be loaded if the Apply visibility settings property is enabled. If empty, the form specified in the Form name property will be used.
Custom registration form
•Alternative form - specify the full name of the desired alternative form (cms.user.RegistrationForm by default).
•Form name - specify the full name of the desired alternative form (cms.user.EditProfile by default).
•Allow user to edit field visibility - check to enable the visibility controls.