Certified Brasilian here (and I did capoeia as a child), I'm sure you already know most of the things I'm going to say, but here are some personal takes about this:
1. Capoeira is a very acrobatic fighting style, which actually matches with Naruto himself
The boy can't keep himself in the ground for long, so he's always jumping around, kicking people into the air.
2. Capoeira is a kick based fighting style, if you watch a Roda de Capoeira you will quickly notice that
And the thing about this is that, if you are using in the Naruto universe, while the characters are jumping and kicking enemies into the air that kinda leaves their hands free to make handsigns and Justus, and that would fit with the Uzumaki clan specially well bc they do specialize in selling jutsu.
So let's imagine a quick scenario base on a imagine for fun:
Let's say the Uzumaki is the guy on top and the other is a random ninja, okay?
So the Uzumaki do a crazy kick, but barley misses the target, because the random ninja was so worried about dodging that, he is in a compromised position when suddenly chains grow around his body, he didn't even notice the Uzumaki making handsigns because he was looking at his feet the whole time worrying about the areal kicks and acrobacies.
You know how Guy learned how to fight Kakashi/Sharingan users by not looking them at the eyes, because he would get into a genjutsu otherwise? It's like that, but the Uzumakis are using their taijutsu, kicks and jumpings to distract their opponent from what they are doing with their hands.
I also really like Kushina using hair for attacks, because a lot of Capoeira is fake movement to hide an actual attack, here's a video:
(this is example video os a technic, I did not find this combo being used in a actual Roda)
You see, he's always tricking the opponent to make it seem is moving one way, when they going another, so is Kushina is using her hair, this pay very well with the rest of the style.
Imagine Kushina is the guy on the top, and she uses her long hair to hit the guy below when she passes by him. It would make a really cool fight and I love it!
3, and most important of all: Capoeira is a fighting style DISGUISED AS AN DANCE
Brief story history here: The slave in Brasil wanted to train fighting to resist against their lords (I forgotten the actual word for it in English), but if they got caught they would be punished, so they make it appear like a dance
The instruments? Battle codes.
And the whole thing about the Uzumakis is that we don't really know anything about them, right?
So hear me out: What if, for the most part of history (at least prior to Konoha) people don't fuckin know theses guys are ninjas?
They see a bunch of red head people dancing and maybe doing some chakra tricks, and they like "Oh, alright they artists or whatever" but behind their back the Uzumaki are doing missions for money just like every other clan at the time, they just so good at it people don't notice.
And it would also explain why people don't know much about them, like beside Mikoto, Nagato, Kushina, Karin and Naruto there's no Uzumaki around, and no big story about a Uzumaki village, heck we don't even actually know if the whole clan was part at Konoha at some point or not, but you know what we have? Temples! With those weird masks Orochimaru finds, in other words: Art, in fact if we're thinking about the masks we can say is a WEAPON disguised as ART, just like Capoeira!
Edit: oh and Hagoromo whole thing for chakra use was it should connect people and not be used as a weapon right?
Maybe the Uzumaki are the ones that kept part of that filosofy, so when other clans saw they use jutsu it's always non combated, but behind their back their dancing and their art, it's all weapons. They just discreet about it either because they were active in danger or because they ninjas and ninjas should hide their true nature and everyone else is just being stupid about with their fireballs and wooden jutsu