lavdavka,
I’m really sorry you feel that way. I daven in a “heimishe” shul, almost every person gets a Shalom Aleichem. i say Heimishe, because I’ve noticed that Litvish or yeshivish are much cooler towards others. BTW i Am an FFB. When I attended the Mirrer Yeshiva many, many years ago, the saying was ” a new guy only gets a Shalom Aliechem by Kiddush levana!”
With regard to saying “good shabbos” to women, it is an inyan of tzniut.
I greet every man in the street, but not women. If a woamn says Good Shabbos to me, and I see that she might be “new” to this, i answer her, so as to be a mench.