DH volunteered in an English as a Second language program a few years ago. One of his students was a woman from France and her and DH talked about her culture. I remember DH mentioned that in France, often people don't volunteer their first names until after they know somebody quite well and it would be considered an invasive question to ask a stranger their first name. If I have my facts straight, I can see why the OP considers it so rude even though it is very common place in US culture. On the same note, in that culture, it would probably feel odd to address somebody you just met by their first name, even if they insisted, because it is considered to be a fairly intimate thing. However, when in Rome do as the Romans do. It would be unfair for the OP to wish to be addressed in a way that makes her comfortable, yet not be willing to respect that wish for somebody else.
As a child, I was taught to use surnames for pretty much every adult. Some of my parents close friends I used Aunt or Uncle and first name. They had a few friends who dropped by the house on a regular basis and they would be the only adults we called by first name. In college, my professors introduced themselves by their title, usually Dr. I graduated college and worked in an academic setting, however everybody in my small office went by their first name. It felt funny at first because I was so used to being the student and using title and surnames. At meetings with other professionals, they always introduced themselves by their first name. It seemed once I became an adult in the working world, I entered the club on being in a first name basis with colleagues, even those much older, and with high titles such as doctorates. I realize other working cultures may be different.
Teachers in the US are referred to Mr. or Ms. (or Miss or Mrs.) Surname while students are referred to by first name. In an all adult working environment, is it rude for a boss or older person to refer to somebody by their first name while expecting to be addressed by a title and surname?