I think there's a time and a place for everything. A time to cut loose and let it all hang out and a time to respect the sensitivities of others.
There is a difference between boisterous (at home, at the park, running around) and being rude (at a restaurant, running around). I think teaching our children appropriate behavior for different settings is important for many reasons, one of which being that it does smooth their way through the world, boys and girls alike. We want to teach our children of either gender how to behave so that they have positive interactions in the world. Your daughter and her friend may not spend a lot of time learning to sit quietly, but it's not like it's not an important skill. Learning to be quiet and listen is very important because it will affect our future relationships and opportunities. My son (kindergartener) has to learn to sit quietly sometimes out of respect for the other children around him because THEY need to hear the teacher's instructions--and he does too. Or because we are at a restaurant and we must be considerate for others. (I abhor the 'run around and do as you damn well please' restaurants which have become popular in my neck of the woods as of late.) Or because his father and I are having a conversation and this is not the time to interrupt.
Learning about our world is a balance of inquisitiveness and interaction and some deference/understanding of cultural norms. When I was a nanny to young girls, I expected the same manners and behavior from them as I expected from the boys I cared for, no more. To talk in turn, to be relatively polite, to refrain from hurting each other. I also ran the girls just as hard as the boys and no, I didn't teach them to cross their legs-- but I might have suggested to wear shorts under their skirts and dresses so everyone's bum was covered, just like a boy.
We can suck the marrow out of life and also learn to be facile socially; as your unschooler gets older, she'll want to know how to be respectful and show deference to those she wants to learn from. I'm sure you will help her with that. I'm not sure what's up with the negative review of the old friend and her family; some people are more staid and have more of a sense of propriety. I'm not sure it's a bad thing, just different from what you value for yourself and your family.
And yes, move your daughter along to friends who have more similar temperaments. That's fine. Just remember that you want to teach her to look past appearances as she grows up and to get to know people for who they really are. My husband calls me 'Ms Pro-priet-tay' jokingly (sort of, I do insist on good manners at the table!)and knows that while I am quiet in a crowd, I can have a lot of fun and cut loose with close friends. It just depends on if you get to know me or not!
(I should add that I think the biggest double-standard comes in the teen years.... current events and attitudes can attest to that. Girls are saddled with a lot of responsibilities which some assume 'aren't the boy's problem', especially when it comes to sexual activity. )