I am on the fence here as to whether you are being unreasonable or not.
I should think lots of people are just being nosey and they don't know how to phrase their question appropriately - which is awkward because its a nosey question and technically none of their business, so they feel awkward about it (but still sufficiently nosey to ask anyway) and phrase it very badly.
I am always interested in peoples backgrounds/heritage/culture, cos I am a nosey sod - I have sufficient brains and manners not to ask unless its relevant or I am aware it wouldn't come across rude.
So - I think when people are just being nosey and a bit clumsy and you KNOW that what they mean is 'what is your heritage', then YABU to keep saying 'Stockport'...
However if they are being arseholes and want to come out with something racist then frankly it doesn't matter what you say they will still be arseholes.
So in your position I would say 'I was born in Stockport but if you mean whats my heritage.... then..... ' you can either tell them or tell them to mind their own business, or ask why thats relevant.
That said I haven't been in that position myself so maybe I would feel differently!
Frequently I get asked why I am in a wheelchair - not entirely comparable but still, because it is none of their business...
If I get funny about it, I make them feel bad and that means they feel bad about 'talking to a disabled person' and then they want to avoid it.. because they might be clumsy and stupid again and make themselves look thick and feel bad...
So I generally give people the condensed version even if it IS none of their business, or if I feel they are taking the piss ill take the piss back and tell them something ridiculous.
It is frankly less effort than being obstructive or confrontational about it - it isn't more or less likely that the person will then go on to be a dickhead about it, if they were going to be a dickhead, they probably already would be and nothing I can say will change that.
But I find generally not getting peoples backs up over them being a bit rude or thoughtless makes life a smidgen easier for me, so why wouldn't I do that?!
So yes they are BU to ask, because its generally rude, but when you know what they really mean YABU to be obstructive about it I think.