In the process of creating a minimal project I finally stumbled across the source of the problem. I was using a CSS stylesheet called 'style.css'. However it turns out that this is a reserved name in C3, so simply renaming the stylesheet fixed the problem.
If you create a new css file in C3 and then try to name it 'style.css' you get a warning and you're prevented from changing the name. However, if you use 'import files', you can import 'style.css' without a warning - beware!