It looks like I didn't fully appriciate the neighborhood my kids grew up in. My girls were "free range" from they were 3-4 y.o., and so were 90 % of the other kids in the street. During the winter time it gets dark around 15:00, so we slapped on some reflectors and gave them torches before sending them outside. We rarely knew how many we would feed for dinner, some days it was 10, other days only us two adults. I never counted, but it seemed like our kids were fed by the neighbors about the same number of times we fed the other kids. Rules were easy to enforce; all the kids accepted that the houses had different rules, and it worked as long as we clearly explained them. Some kids needed a bit stricter talking to than others, but nothing out of order. If they wouldn't behave, we sent them home, and if they thought we were too strict, they ran home. But they always came back. In this neighborhood, only one family insisted on making play dates, and that kid was soon left outside from the other kids' games. It was much easier to run to one of the neighbors, instead of going back home to get us to make arrangements. After a year or so, those girls were also let loose when the parents realized the other parents really didn't want to go through the hazzle.
This is obviously not the kind of neighborhood/child rearing the OP wants. And that is fine. Their life, their house, their rules. I just wanted to tell about a different way to see things, and give a hint that maybe the other parents aren't doing this out of spite, but rather because this is how they grew up, and this is the kind of childhood they want their kids to have. A bit strange that they turned the OP's kid away the only time she asked to visit, but it could have been bad timing. Or they might be selfish idiots. That is always an option.
When we moved to a larger city in a different part of the country, we probably came across a bit like the "bad" family the OP describes. In this neighborhood, playdates are much more common, and parents tend to panic if the kids aren't home straight after school. Our kids are used to freedom within boundary, so we don't need to keep a tight leash on them. They will be home at the agreed upon time, and stay within the perimeter we have told them is safe. It didn't take long before we had to start driving other kids home when they drifted to our house, because it was clear they weren't, and couldn't be, trusted by their parents. If my kids visit someone after school, they have cleared that with me beforehand. The kids we got visiting in this area were lying to my face, telling me their parents knew where they were, when in reality they were calling the police because their kid was "missing". If that is what you are used to setting boundaries for, I understand that it looks strange when a new kid knocks on your door and asks if they can play with your kid. There are also kids in this area who arent allowed to walk outside it there is snow and dark. I'm sorry, I try not to judge, but we live in Norway. Keeping children indoors 8 months a year isn't healthy.