Out of curiosity, can you explain what effect you believe this might have?
I am glad to be wrong, but I feel like most white people in the USA wouldn’t be offended or even find that to be a strange question. They’ll just answer it as best they can: Florida, Sacramento, born in Boise but raised in Fairfield. Or if you press about ancestry, most white folks will gladly say French-German, Irish, etc and then maybe even ask you the same thing because they’re genuinely curious and because it’s a natural way for an otherwise polite, as you put it, conversation to steer once the topic has come up. Probably most wouldn’t even recognize if another person were asking that question specifically to make a point about racism/prejudice/etc.
I really doubt that many white people have had these types of questions weaponized against them so unless they are made aware of how offensive it can be or how it betrays their own biases/prejudices (which we all have by the way), they may not even know. I would think that explaining how those questions impact you negatively in a supportive and understanding way will get you much further with most people than being retaliatory or intentionally inflammatory.