I'd also find it a bit odd to ask this in a business situation. If you were in a friendly informal conversation it might be a bit different. However - generally speaking we only ask about people's background if they have an accent that is obviously 'foreign'. Then you can say something like 'so where are you from originally?'. If they have the local accent then it would be a bit insensitive to start questioning their heritage. After all, in Europe (especially in the UK) we are so mixed up that you could easily have someone with a 'foreign' surname who has no idea why - it could have been an ancestor hundreds of years ago. If someone has a 'foreign' name for both their First (given) name AND their surname then you can probably assume their parents come from that country, and it's not such a big deal to make an informal enquiry - but I still wouldn't raise it in business.
With regards to people who look mixed race, no, it is rather inpolite to ask unless you get into the sort of informal conversation where it is natural to talk about our backgrounds - but I wouldn't single someone out. I do know a few mixed race people and some of them I know about their background, and others I don't. Somehow sometimes it just comes up naturally - usually they start the subject off. For example, I found out that one mixed race girl had a Trinidadian father when she started talking about a trip back there to meet some of her family. We then had a good chat about her trip and her family. But I wouldn't have asked 'where are your parents from?' just out of the blue. To us it sort of suggests that you feel they don't fully belong here.
We also don't really approve of asking strangers personal questions on any topic, not just race.