You can allows your BuddyPress site members to turn their avatars i.e. profile pictures private, keeping them only visible to friend connections and not other members and guests on your BuddyPress social networking website.
BP Private Avatars is the new BuddyPress plugin that allows all website members to turn their profile pictures private and limit their visibility only to friends.
Start by installing ‘BP Private Avatars’ plugin in BuddyPress
Upon activation, members may simply go to the Profile Settings and choose ‘Make Profile Photo Private’ in order to hide their avatar on website.