This question is different from this excellent one, since it is not about tourists. The differences will become clear later on, I hope.
I will, as usual, use fake names (Alice and Eve this time) and also name places (L. A. and New York), that do not need to coincide with the actual cities.
Alice is a US citizen, born and raised in the US. Her name is very uncommon, though. And her appearance doesn't match "Average Jane's" entirely.
Eve is nice and open-minded and looks more like your "Average Jane".
I met with Alice and Eve, who didn't know each other before, in New York. I do know both, so I was the common denominator. It was nothing formal, just a nice evening at home.
After some introduction, like where I met Alice and Eve for the first time, a dialogue between Eve and Alice ensued:
Eve: Where are you from?
Alice: I'm from Los Angeles. My whole family lives there.
Eve: I love L. A.! But where are you from originally?
Alice: (short pause) Also L. A., I was born there.
Eve didn't seem to notice anything, and they went on. After hearing the question, I looked at Alice to see her reaction, and, although it was subtle, I do think that she wasn't glad about "Where are you from originally?". Also, she seemed a bit more reserved afterwards. On a sidenote, Eve also told a lot about herself, it was not a one-sided questioning.
At the end, Eve said, that it was a nice evening and Alice was great, but maybe a bit distanced. I said, that I felt that question to have been rude. She disagreed, noting how I was being over-sensitive and how she loves foreign cultures. She just had wanted to get to know her better and was genuinely interested.
Now, Alice was polite and said that she had enjoyed the evening and how Eve was a nice person. She didn't complain, but I doubt she would have, fearing it may hurt me. I also didn't want to pressure her for the sake of my couriosity. So I just gave her the chance to voice her opinion, in case she wanted to, and decided to ask the community here.
Is it rude to ask someone "Where are you from originally?". Is there maybe a better way to phrase the question?
Please note, that this is not about proving me and my reasoning right. I'm genuinely interested in how such a question is perceived. And this is, in contrast to the other question, not about tourists or the like. While Eve didn't know Alice, there was no reason to suggest, that she was, e. g., a tourist. And there may be cases, where just the name is very uncommon.
Average Jane: Someone you'd see in a TV ad representing the audience