This is a policy decision dating back to IIS 6.0.
The fix is simply adding the unknown mimetype to the web.config for the Azure Web App: https://www.iis.net/configreference/system.webserver/staticcontent/mimemap
For example:
<configuration> <system.webServer> <staticContent> <mimeMap fileExtension=".dwg" mimeType="application/acad" /> </staticContent> </system.webServer> </configuration>