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.
In your original comment that I responded to, it sounded like you're making the case that mixed and non-white people should start asking white people those questions as a matter of policy, and not just those times when a specific white person asked first. That's why I was curious what you thought the effect would be.
That being said, even if you meant that people should only return the question if the white person asked first, that's something which would just be normal and instinctual for most folks, I would think? Like if someone I'm getting to know asked me my favorite color, I'd probably follow up with the same question after I gave them my answer. So it seemed a bit weird to see a call to action to do something that I would have otherwise thought most people would already be doing (at least in my experience, which I certainly am open to the possibility that my experience is atypical of what racial minorities endure).
And although I am white, and thus I'm certainly coming from a place of privilege, I am a minority (lgbt) and have had my fair share of experience with inappropriate and/or weaponized questions, so I'm not coming from this from a place of complete naivety. I'm certainly aware that sometimes people will ask questions like "are you the boy or the girl in the relationship" from a place of authentic and unintentional ignorance, but that it's quite often coming from people whose intent is to be derogatory.