BuddyPress.org

I’m confused you don’t seem to have any buddypress components in use at all. If you visit the BuddyPress menu in the backend admin under ‘Site Admin’, you’ll see an option to turn on the admin bar: Show admin bar for logged out users: yes/no.

Yes would turn it on and allow visitors the option to login or sign up. If you don’t have that turned on then how you log your users in is entirely up to you.