I have the same error when calling one of my custom services using Postman REST calls:
Hi Stephane & Tim,
Content-Type cannot be null in ThingWorx. It tells the server what kind of result to resqponse to the client. If it's null, server cannot decide which type of result to return to the client.
So in Stephan's use case the URL should be Thingworx/Users/[UserName]/Services/GetOrganizations?method=GET&appKey=...&Content-Type=application/json
Below screenshot is my test result.