Jo,
The same thing still happened as recently as two years ago in Chicago. People who had never been out of the US told me in all seriousness that they were Irish. I found it very confusing.
As for asking where people are from, I'm not sure that I found it an especially big deal when I was still living in the UK. I think it's to do with how you ask. Forget what colour someone is - if they talk the local language fluently with the local accent, assume they're local. If they talk the local language fluently with a non-local accent, ask a neutral question. 'Have you lived round here all your life? / How long have you lived round here?' They can answer with the name of another city or another country as they choose - and as is appropriate. This stops it being a nationality or ethnicity question and makes it a question about the person.
It also stops it being a question about their family's origins in Ireland when you're standing in the middle of Chicago!
