The problem is to do with how the external dependencies (like FontAwesome) are being loaded.
When I look at the Web Console in Firefox, it seems that it’s trying to load the dependencies for the test server
Blocked loading mixed active content "http://localhost:1313/dist/fonts/fontawesome-webfont.eot?#iefix&v=4.7.0"[Learn More]
Then have a look at the css file which Hugo builds there’s loads of references to
I’m not familiar with building on gitlab, but my guess is the mistake is somewhere in either how the extended version of hugo works with gitlab pages, or with what you’re pushing into your git repository.