Xcode uses Clang/LLVM to compile Objective-C (and used gcc before adopting LLVM). To my knowledge there's nothing closed source involved in the compiler. I had Clang/LLVM compiling Objective-C on Linux a long time ago. Visual Studio for Windows has been able to compile Objective-C for about a year (see https://developer.microsoft.com/en-us/windows/bridges/ios).
Objective C has not had an official open source release, so far as I know.
ETA: Arguing of course how close the gcc/clang implementations of Objective C may or may not be to the Xcode compilers, of course.