“you know what, i don’t think i would like it if a random girl on the street greeted my husband”
There are greetings and then there are GREETINGS. A simple good Shabbos, should not be out of line for anyone, but if anybody feels offended, they need not look up, but they can nod their head or mutter good shabbos in return, just to show derech eretz and ot embarrass another Yid in public.
(Just as a sidebar) : My dad once told me an interesting D’var Torah of why when we say “Sholom aleichem,” to someone, the response is in reverse, “Aleichem, sholom.”
Again, I do not recall in whose name this was said originally – but the reason that he was told, is that when Whe are makdim someone b’sholom, which is Hashem’s name, specifically because we are being makdim, we have a special shemirah on our health at that given moment. The person who was not makdim b’sholom, has no such shemirah on himself, therefore if he said Hashem’s name of “Sholom” and something happened between saying the Name and saying the word “aleichem,” he could have said Hashem’s name l’vatalah. At the time my dad told me this, he was trying to impress on me the idea of not making a bracha l’vatalah, that the Shem in any form is holy, and even when greeting someone, we must always be cognizant of that.