If you set the view members profile permission for the Unregistered group to Not Set, that would hide the list in the sidebar. I just tested it and the heading is not shown as well. As it shows in your SS, then that may be a style or add-on issue.
You have posted in the Widget Framework thread, which suggests that you are using that add-on to display New Profile posts and other sidebar stuff. You will need to ask in the discussion thread for that add-on for a solution as the above may not necessarily apply as it's for the standard sidebar.