Both my son (5) and daughter (4) are like your kiddo, OP. My son for some reason seems to get replies back much of the time he says hi to other kids, but DD rarely if ever gets a positive reply, and she's been starting to be sad and say things about it like "no one wants to play with me" and such. We're starting her in preschool in the fall specifically to get her some social time.
I think it is a cultural phenomenon where many parents have such busy social lives and schedule playdates and classes and even homeschool groups that they train their kids to only play with the kids they're scheduled to interact with. I think in the past, when parents didn't do all this scheduling stuff all the time, kids were just, I don't know, not expected to be best buds with other kids, but it seems that if they lived in the same town or neighborhood or something, they could at least say hi to one another. I mean, how else did whole groups of kids get to know each other, play neighborhood games, etc? It wasn't mommy making a playdate with the kids down the street. As for us, our family just doesn't DO mommy and me groups, scheduled classes, things like that. And we have moved so often and to new areas that I personally have zero mommy friends right now, so clearly no other families to get together with. So... how are my kids supposed to meet other kids, again?? Why am I supposed to make friends for them when in generations past the kids were perfectly able to make friends for themselves, generally speaking? Maybe not at age 3, but at age 5, 6, 7? (Obviously this is more asking in theory than really asking that personally, but you know what I mean.)
I have actually posted on here a few years ago when I had a mom say to me at a neighborhood playground (the week we moved into a new neighborhood) that they don't go to playgrounds to make friends, they go to play with friends they already have. I didn't even get why she would say that. I didn't get up all in her business and ask her to be my bff, I made one small-talk type comment about her daughter who looked about the same age as mine. I guess she got offended I said anything to her at all? Well, fine. Don't be friendly, then. Even the ladies at LLL meeting I went to specifically to meet other moms already went with their mom friends and weren't looking for new ones. I'm just as confused as my daughter is by the unfriendliness of some people. I am an introvert too, believe it or not, and I certainly don't go pushing myself on people, but there are times when even just saying a pleasantry seems to offend others. (As reinforced by some of the responses on this thread...) It is cultural, and I'm a little confused by why culture is heading down this road. But oh well.
I think it's a parents' job to teach social skills. For parents of kids who are too friendly, that means teaching how to respect social cues, not be pushy, etc. And, for parents of intense/busy/whatever kids, that means teaching them how to be polite and say hi back to other kids. It's a learning process. Adults shouldn't consider other kids rude. If anyone was rude, perhaps it's the parents, if they don't say something to teach the kids. Yes, there are times when my kids are "rude", but I try to make being in public a learning experience. How we deal with others. Not being pushy, not being unfriendly to the point of impoliteness.
I am really surprised that if someone came up to someone in a farmer's market and said hello to you, they would consider it OK to not say anything back. I understand not getting into a full on conversation. But if someone's going to make the reach to say hello to someone, I can't imagine just staring at them and walking away. I also admit that I don't fully get the whole "are you sharing an experience isntead of sharing the same space" if you're on the playground or something. Yeah, you're sharing the experience of playing in a public playground. I wouldn't walk into someone's yard and join in on their pool party no matter how much fun it looked like. But if my kids are playing at the local park, and they want to interact with the other kids there, why do some parents think that it's somehow intrusive to their kids if mine say hello? It's another thing entirely if your kid made clear that they want to be left alone to build their sand castle, and mine were to follow them around and pester them. (They wouldn't, btw.) But just saying hello? That's bothersome?
If your kid has special needs, that's DIFFERENT, and I GET THAT. (My own son has SN. And he doesn't always "look" like he does, so I always keep an open mind about any other family and don't judge, because you don't know what's going on. Even if there isn't a SN, the kid might be tired or sick or grieving or whatever!) But if your kid is just the type of person to be busy in what they're doing, then please teach them at least what another pp said - to say "hi, I'm busy right now, nice to meet you but I'd rather be left alone." Props to that. But to condone them ignoring other kids is rude, imo. Are they always going to act perfect? Heck no. But it's a parent's job to at least TRY to get them to understand that ignoring others isn't kind.
Before you come at me that I couldn't possibly understand the sensitive child - I *was* that sensitive child. This post is coming from a person who was PAINFULLY shy as a child. I was constantly "embarrassing" my own mother because for the longest time, I wouldn't say hi to anyone, even her friends. So I get it. But she kept at it because she viewed it as her job to teach me how to at least be polite. And eventually it sunk in.