I figure that I as a white person, growing up in an area that was 99.9% white, I really can't say what is or is not offensive to other ethnicities/races. To me, and to everyone I know, any question asking about heritage is totally acceptable. All variations of "what are you" are fine. It's not loaded where I'm from.
But I know that my very German blond haired, blue eyed Grandfather got irked when my aunt and her husband (a more dark-skinned man of Slavic heritage) had a son. His sisters asked, "Is he dark?" and Grandpa snapped at them for asking such a thing, because he felt that they implied a judgement, that being darker would be undesirable. His sisters are kind of like that... so I guess the context matters. He felt that their question was "loaded."
Anyway, I asked my husband, who actually is a minority, if it bothers him, and he went back and forth. At first he said, "No, why would it? I just answer." and then he said, "Well, I don't like it sometimes..." and then he said that basically, the question by itself wouldn't bug him, but that under some circumstances (like, depending on who is asking and why) that it could.
I am basically (because of my 99.9% white background) just really afraid of being offensive without meaning to. So I try to steer away from ANYTHING that would indicate that I'm focusing on color or ethnicity.
: To the point of being overly PC. So I wouldn't say "What are you?" or worse, "What are they?" in reference to someone's children. I'd say, "What a pretty little girl!" and move on.
But in some instances it's helpful. We have some Asian neighbors, whose daughter is good friends with our daughters, and all I knew is that they were not Japanese or Chinese - I would have recognized the language, and it would have been easier to get to know them because we have a bit of understanding of Chinese culture, and more about Japanese. I really really wanted to know, it seemed like it would be helpful in bridging the gap. On the one hand, I want to honor that there ARE distinct cultures in Southeast Asia. On the other hand, I don't know how to ask. I found out from the daughter in as roundabout a way as I could. (Laotian, if you were wondering.)
I had a friend in college that everyone assumed was AA, when in fact she was Hispanic (Dominican.) I think she actually appreciated it when people asked what she was, because it showed a lack of assumption.
My grandmother always used to say that biracial babies were the most beautiful babies possible... I wonder if that is offensive? I don't think she would have said it in front of anyone other than immediate family, but she was very sincere. It just made me uncomfortable to even have race mentioned. Which I know is silly - because my family really appreciates diversity. But - I guess because I know that they were even more insulated than I was, just by circumstances - that they naturally will have a bit of ignorance in how to be sensitive while still being comfortable. I got burned in college in a history class, in my bright eyed, bushy tailed freshman year, when talking about slavery in the US - and I was talking about the plantation owners viewing the slaves like cattle... and somehow this one AA girl got the idea that I was saying that blacks are like cattle. I was mortified, it was the worst feeling. I still to this day don't know where I mispoke. If it had just been her, I would have thought she was simply mishearing or very sensitive about it, but several other AA students were also angry, so I can only assume I was ignorant in my wording. I still can't think of it without a bad feeling in my stomach, and it's been over a decade. My professor fortunately got what I was trying to say, and helped me feel a bit better, and I posted a formal apology and explanation that I didn't think anything like that. It blew over but I was traumatized.
This was all very rambly, mostly I'm just trying to figure out what I'm thinking. I just would never talk about heritage with anyone who wasn't white, unless they brought it up first. And then I'd be very interested in what they had to say. I'm not sure I'm expressing myself very well, it's 2:30 AM here!!
(While I liked my childhood, and feel like my family did a wonderful job of instilling in me a love of diversity despite the insularity of our area - I am SO glad that my children are growing up with more exposure to different ethnicities and races and cultures than I had. Less self-doubt, more connection.)