Greeting Women
Question
Are men permitted to greet women?
Answer
Shalom!
Thank you for your question.
The Talmud teaches that “one may not inquire [she’eilat shalom] about the welfare of a woman.” This form of greeting, “she’eilat shalom, ” generally refers to greeting others with the words “shalom aleichem.” Greeting a fellow Jew in this manner was instituted by the sages so that Jews would greet each other using one of G-d’s names (Shalom).
It is said that greeting people with “shalom Aleichem” brings people closer together. As such, a man should not greet a woman with “shalom aleichem” so that they do not become overly social with one another. Therefore, a man may greet a woman with “good morning” as this does not bring people closer together in the same manner as “Shalom aleichem.”
Of course, one must conduct oneself approrpiately when interacting with women and limit all greetings to acts of common courtesy and not as gestures of friendship.
Source
Kiddushin 70a; Aruch Hashulchan, EH 21:8.