Penar, big big big sorry:
I compared settings on our productive instance (PROD) with the ones on the DEV instance. Only the DEV instance had disabled the force_https setting. And this only worked because we have the SSL haproxy SSL accelerator in front of it.
I now activated the SiteSetting.force_http n the DEV instance and discourse ID works fine. Thus I will also deploy Discourse ID on our PROD instance (forum.netzwissen.de).
Sorry for the confusion.