YANBU and some of the being vague suggestions have been great. I find they work for most people and can take a load off, but there will always be the ones who won't drop it.
I'm not sure whether to laugh or roll my eyes at all the 'embrace yourself' bullshit and the whole 'people are just interested/you're really not that interesting' dividing line. I can be quite happy with myself and not want to have the same conversation with strangers repeatedly.
I do not get how others don't understand why some people might not want to talk about where we're from at any moment with random people or view the impact our accents have on our lives on as unfortunate. I mostly get these odd questions from people on the street I wasn't even talking to or people I've just met that I'll likely not be seeing again, not the collegues or those I've known for a bit that I would understand it from. Yeah, it's not my address, but as someone who left my birth country under not the best circumstances, I'd honestly rather discuss my limp, but most people are far too polite for that.
It's awkward to just be out with my family or friends and have it stopped because a stranger has heard me speak and feels they now need to interrupt my day to ask questions. Sure, it's cultural, but I'm not a cultural landmark, I'm a person who might want to relax or is having a hard day. It's even more awkward when I'm at the chemist or with a professional who feels that need and my or my kids care is paused for those questions because "oh I knew I heard an accent" with a twinkly laugh like they've figured out a secret anyone else who can hear already figured out rather than discussing anything actually relevant.
Honestly, at times, I'm just grateful when it doesn't lead to a political conversation. Or being told my son's stammer or trouble with English is because of my accent/background. Or when people want to know why I still have an accent after living here so long or other question I really don't know how to answer. Or people mimicking my accent to be funny because I just sound so funny.
Yeah, can't possibly see why I might not want to talk about my accent and where I'm from with people I don't know in person. It's not personal at all and just like discussing the weather - oh wait, I've had strangers tell me how I can't complain about the weather because "it must be so much hotter where you're from" or "you chose this weather over..." So yeah, the assholes make everything horrible.