Are "mostly POSIX-compliant" systems still considered POSIX systems? Irix and OS X are POSIX systems because they are fully-POSIX-compliant. However, operating systems like FreeBSD, Haiku, and GNU/Linux, for example, are "mostly-POSIX-compliant". Can people still correctly refer to such systems as POSIX systems?

No. The Open Group has an actual POSIX certification process, so if an operating system hasn't been through that, it cannot be referred to as POSIX-compliant.