Hello JMB,
In order to set user profile private to all unregistered user, you may go to your joomla backend > easy social > profile type > click on the registered user shown here in this screenshot
http://screencast.com/t/ql19rCGNT7RW > go to privacy shown here in this screenshot
http://screencast.com/t/kOkhfSGmwl .
From there you may set the user's profile viewable for registered users or friend of the user.
Hope this answers your question
Regards
Kheng Wei