BuddyPress.org

I’m not sure what you mean – but according to https://codex.wordpress.org/Function_Reference/wp_nav_menu you could have ` ‘fallback_cb’ => false,`

I don’t know how you are doing the mobile menu, but couldn’t you just have $current_user logged in and out mobile menus?

If someone can guess the page such as activity, then just hiding the menu won’t stop them getting in anyway.