Images in sites/default/files are not allowed to be seen anymore
Ok, so I found a solution that worked for me. 

In the process of investigating in this problem and the fact why it does not appear on other Drupal installations I have running on the same server I messed up the permission settings on my server. In order to reorder things, I installed the module https://www.drupal.org/project/security_review - it produces a list with potential security problems of your Drupal installation. I worked myself down the list solving the issues one by one. I am not sure if this was the point in the beginning but after I changed the permissions of the .htaccess-file in sites/default/files to 444 (readonly) suddenly my images were accessible again.

For your reference, here are a lot of other approaches you can try if the one I presented is not helping: https://www.drupal.org/node/1170440