I am looking at a project that is built with Clang but it needs GCC headers.
Why would a project require both Clang and GCC headers?
By default, clang builds with the standard library installed on the system, so objects can be linked with libraries/programs built by other compilers. If you have installed libc++, you can use it with the flag -stdlib=libc++
.
For more information have a look at the documentation.