I'd ask anyone of any colour so yes, I still think that's not a "bloody offensive question". Of course, "yeah, but where are you from originally" is offensive.
Herecomes, but your original question was 'where are you from /and your parents?'. How is asking where someone's parents are from any different than asking 'but where are you from, originally?'
I've also spent much of my adult life overseas, mostly working in international schools where 'where are you from' is asked a thousand times a day without anyone taking offence. It's a fair question, in that context, or in any other context (expat groups, holidays) where you naturally assume the person you're asking isn't from 'here'.
It's entirely different when you're repeatedly asked it in your own home country. At best, it's individually well-meant, but also repetitive and intrusive; at worst, it's used to make some pointed comment I'm asking because clearly you're not from here, you don't get it or racist assumption.
I'm white British and used to have an Anglo surname. In the UK, I got asked questions about my origins perhaps once or twice, probably during Freshers' week at college or when moving into a new house. Now I have a very forrin surname, I get asked about it constantly. It didn't even bother me, at first, but a decade on I'm getting tired of having to either answer personal questions or deflect interest. It's also a bizarre sensation being scrutinised for your ethnicity when you've barely considered it before -- having had the privilege of considering it a non-issue, really, being white in a majority white country. Now some people actually look me up and down, saying stuff like:
- but you don't look [ethnicity]. You look more... [Greek/Irish/any random choice, including, memorably, 'a bit Chinese']
- you're from [other country], though?
- oh, I see. Born in England? And your parents?
- your married name, right. So you met your fellow on holiday, there?
- he's from Watford? But where's he from, originally?
WHY am I having this conversation? I only wanted to buy a fecking laptop -- why are we now discussing my father-in-law's emigration? This is madness. But if I ignored your questions, I'd seem snotty; if I explained why I can't be bothered answering them again, you'd probably repeat the same BS about some people 'looking' to take offense.