I say Good Shabbos to everyone, man or woman, and if a man, do not look at him directly. I answer GS to anyone and everyone who says it to me first. My husband says good morning to non-Jews in the street on the way to shul. They ALL answer him back in kind.
People should stop making such a cause celebre out of this, in my opinion, and we will all be happier. Saying GS is only a tznius issue if you believe it to be. When it says hevei makdim es kal haadom b’sholom, it did not say, “unless you are a woman.”