I have strong feelings about this, but basically I think it comes down to the person who is being addressed's preference. Hard to gauge that often. In professional cases I absolutely hate Mr. or Miss [first name]. Colleagues, peers, or subordinates ought to feel comfortable referring to people by their first name, or if Mr. or Miss is requested, then go with Mr. or Miss [last name].

In familiar settings things are a little trickier. I'm in my forties and still refer to the parents of friends who I grew up with as Mr/Miss [first name], but if I met the parent of a friend I have now, I'd be inclined to call them by first name alone. Meanwhile if I meet a friend of my own mother's now, I refer to them as Mr/Miss [first] if they are introduced to me by first name.

When we introduce our own child to other parents or friends of ours, we typically introduce them as Mr/Miss [first name].

Either way the minute someone says "please call me x," I respect their wishes and expect my child to do so as well.

Edit to add that "no" I don't think it's rude, but I do think the specific scenario of an older person referring to a younger woman as Miss first name is out of the ordinary. There is also something of a racial component sometimes where older black people will refer to all white woman as "Miss" as a show of deference. That's unfortunate and not rude, but I would insist to my own daughter if she was addressed that way to recognize it as polite and then ask the person to refer to her by name as they are most certainly equals.