Please don’t excpect a chassidishe man to say good shabbos to a MO woman on the street or in Shul.”
It is rare for a MO woman to say GS to a chassid. Only someone who really does not understand the “etiquette” of this would say anything at all spontaneously to a chassid. But being a bulvan is being a bulvan. If someone greets you, you can respond quietly, briefly, and in a low voice. Otherwise, it is mevayeish someone in public, and THAT is b’feirush a Lav D’Oraisah, whereas saying Good Shabbos to an opposite gendered person is NOT, NOT, NOT. And if you believe it is, show me the exact makor that is accepted by all frum Jews, that specifies that saying Good Shabbos is assur.