Hi Philipp,
I'm not sure if someone has corrected something since you posted this, but in both cases, I don't get the behaviour you describe.
In both cases, you get an "Error:Forbidden" if you're not logged in.
Can you confirm that this is what you're seeing now, or have I misunderstood your report?
That said, the error page also contains a "You are currently not logged in. You may want to do so now", with a link to the wrong login page (the Trac native login one, rather than the Github one). I'll look into this.
Yours,
Russ Magee %-)