Thanks Jörg, that did the trick. Nevertheless I reported it as a bug since the configuration dialog says "additional HTTP headers" - so it implies that the default headers are not getting replaced.

When configuring an additional HTTP header for a replication agent the replication breaks due to the necessary standard headers not being sent anymore.Replication test without additional headers (see the three headers):Create new HttpClient for Default Agent* Auth User: replication-receiver* HTTP Ve...

I'm facing the exact same issue with AEM 6.1.0 SP1. Does anyone have an idea?