It doesn't seem to be a super common, general thing where I live. However, there are some more prone to it than others, like places that have a bar and/or otherwise serve alcohol. Typically though it's only the nights they do live music and that's most often weekends and around specific holidays.
Mostly I just avoid pretty much any establishment if they've got live entertainment for the night and I'm there to eat as well as talk with others. I avoid any that are particularly egregious in terms of loud music. I have been with a group where we asked if the volume could be turned down on the speakers one night at a live event where we were one of only a few tables in the entire place and it was clear that nobody was particularly interested in damaging their hearing. The manager slowly slinked over to the performers about 5 - 10 minutes after the request, and they stopped playing shortly after.
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.