How to make Linux Docker image filesystems case insensitive?

I have a Docker image for cross compilation from Linux to Windows with Mingw-w64. A common issue is that source code and build scrips do not refer in lowercase to filenames. (windows.h/Windows.h, libUser32.a/libuser32.a …)

Is it possible to make any access to the filesystem or some directory in a Docker container case insensitive?

Source: StackOverflow