If it had been a 4-year-old, I'd say it was just a kid repeating what s/he had heard. But a 9-year-old should have been taught that it's OK to disagree with someone's personal choices but it isn't OK to give unsolicited advice to them. I know my 10-year-old knew last year, and probably for at least 2 or 3 years before that, not to do anything like that. And she isn't great at holding her tongue.
Though I suppose it's possible the letter writer had misjudged the child's age.
This is my gut reaction as well. If this were a babbling 5 year old, I'd be more inclined to agree with Abby. Kids that age say stuff all the time that would get them in trouble if they were an adult. Their parent/guardian should of course gently correct them, but I can't really fault them for taking a little while to really "get" what is okay to say and when it's okay to say.
If it were a 17 year old I think we would have a pretty clear consensus that the 'child' was rude. Somewhere in between the line blurs. I feel like by 9 I knew that you couldn't always say what you thought and that you needed to be polite to people and respect their personal choices. So I do think the kid was rude. But I also think it's more forgivable for a kid that age, simply because we all do and say dumb things - and I think that age group in particular (between "innocent by virtue of being a child" and "adult that absolutely knows better") is particularly prone to them simply because they lack more life experience*
But I do wonder if the LW was actually smoking when the kid approached her. She doesn't mention it in the letter (although the signature suggests she is a smoker). While there is still something off about approaching a stranger and saying "Don't Smoke", if she wasn't smoking then it could have been meant more like "Vote For Candidate A" instead of "Stop Doing X (which I think is bad for you)". Because I wouldn't fault a kid for generically handing out anti-smoking/smoking kills propaganda (with the stores permission), but accosting individuals randomly or because they are smoking is off.
*Not intended as an insult, I just know that I said more things I later regretted at that age than I do now. Part of learning and growing is screwing up.