The default behaviour of Jenkins is not to force a login.
The default behaviour if you don't have permissions and are not logged and request a restricted page in is to redirect to the login page to *start a login*. By default this is the username/password form, but this can be changed by the Security Realm which is the case here.
There are several things here that are important - note the "restricted page"
on logout the realm is redirecting to the root of Jenkins which may well be a restricted page depending on your security setup.
So there are 2 things that you can do.
1) change the login to take an intermediary form that requires the user to take action (ie a separate Login with GitHub button)
2) do not redirect to a page that requires authentication when you log out.
I went for option 2 as in the normal use case it is one less button to click.
Not sure what point you folks are making. The default behavior of a locked down Jenkins is to force the user to log in. In the case of OAuth, the user is automatically logged in via OAuth.
I've clearly explained the use of the logout link and what happens when you log out (to be automatically logged back in). Additionally, if user or team membership changes the logout link still serves a purpose.
If you want the user to be officially "logged out" and to show a "login" link then the only way possible is to allow Overall Read. The core behavior is not going to be changed.
Closing this issue... again.