Last week two missionaries were adamant that they were not going to call her "Priestess" but also would not agree to first names or Mr last name, yet they insisted that they still be referred to as "Elder."
Does your friend regularly engage LDS missionaries in conversation? I'm curious, because while some missionaries/proselytizers have introduced themselves to me by name, I never got around to giving them my name or title, or using theirs: "Sorry, guys/folks, I'm not interested."
But given that they did have a conversation, they were rude for insisting on "Elder" if they weren't willing to use her title in return. I wonder if they'd have done the same thing with a Catholic priest, a Protestant minister or a rabbi.
Since HIPAA (the very strict health care privacy act here in the U.S.) came along, I've seen some doctors get borderline paranoid about being acknowledged by their patients in public because Shhh! Nobody's supposed to know you're my patient!
It was different back in the day when everyone knew who the local doctors were, so people could have any number of reasons for calling Dr. Jones "Dr. Jones" in public -- they worked at the hospital, they lived in his neighborhood, they went to school with his kids -- that had nothing to do with whether they were his patients. And what if they were? Half the town was.
I'm between physicians at the moment, but if I had an ongoing professional relationship
with one, and I met him/her at the gas pump, the conversation would probably contain no names at all. "Hi!" "Hey, how ya doin'?" "Fine, and you?" "Fine, thanks ... lovely day, isn't it?"
It occurs to me that I don't use names all that much in everyday conversation, unless I'm performing an introduction, trying to get someone's attention, or trying to be clear to a third party whom I'm talking about. My doctor may have invited me to call him Dave, but if I'm calling his office, I'm going to say, "I'd like to make an appointment with Dr. Jones."
I have no problem calling clergy members by their titles even if I'm not of their faith. I was religion editor (among other duties) for a newspaper and knew all the local clergy by name -- from Pastor Smith, Father Jones and Reverend Harris* to Rabbi Bloom, Father George, Jean and Donna (the last two were ministers I knew outside the church context).
In college, all the instructors were "professors" or "profs" in casual conversation. Many of those whose actual title was Lecturer or Instructor instead of Professor would ask students to call them Doctor ___ (if they had a Ph.D.) or by their first names.
*My copy editor's soul dislikes "Reverend" because it's so often misused. It's an adjective, not a noun. It's The Reverend John/Joan Harris, and never, ever "the reverend" or "s/he is a reverend." But if Mr./Ms. Harris preferred to be called Reverend Harris, that's what I called him/her.