I think it's a difference of interpretation. I don't see those as "personal" questions.
This may be the minority opinion, but I don't think someone asking where I'm from is the least bit intrusive.
You are not alone.
And sometimes if you're just not in the mood, then use brevity in your answers. Most be people get the hint. I wouldn't lie.
Lies can backfire on people. What if later you and this person hit it off and become friends? Then ya got some backtracking to do.
Probably gonna get some stick over this, but I would like to point out another observation that may contribute to people asking you when they hear the American accent and this is only my observation...
Americans tend to open up and give you their life story shortly after meeting them compared to other nationalities. American, as a rule, are very friendly. So it could be that they know they can ask and they will get answer. They will get conversation. It's good to talk.
Can I recommend Bill Bryson's books? Look at his views of living in the UK and travelling from an American married to a English woman. He's good.