How do I hide navnar menus from non-logged in users

I have the stranger setting set to "none" no access to content. Which does a good job of locking my sites down from non-logged in users. This only gives them access to the registration page, which is what I want. The only problem is on the registration page all the nav bar menus are visibile. It doesn't seem to be enabling any protection on the nav bar.

I tried changing the stranger setting to an actual role, then set security on that role, but it doesn't seem to do anything.