I remember recently greeting an Orthodox Jewish woman’s hand. She was a rabbi’s wife. She refused to shake it. I was rattled at first, and then remembered that this was proper behavior for a woman in her position.
Jennifer Bryson is a friend and scholar of Islam. Here is her fascinating reflection on being rattled when a male employee refused to shake her hand. http://www.thepublicdiscourse.com/2016/06/17151/