It will show because you allow guests to see the user list.
Control Panel » Group Management »
Guests Site Permissions
First option is
Can view the Member List
set it to 0 for guests.
Then both the user list and self search will only be visible when logged in as a user.
Thanks. I want Guests to see the User List
How can I put it between My_Stuff and User List, instead?
Or between Calender and Active_Topics?
Can I make the Calender disappear for Guests?
