I'm a local, and I wear the same things to the park as I wear all the time. That's Birkenstocks or boots, a dress, and then layers depending on the weather (light weight scarf, cardigan, hoodie, etc.) I also wear a brimmed hat almost every day, whether I'm in the park or not.
I think the difference is that, for a local, our everyday wardrobe is already calibrated for a day spent out and about in Southern California. Everything I wear is already suited for the sun, big changes in temperature, and walking outside all day. I compare this to when I lived in Chicago and Philadelphia and it was normal for me to only be outside when I was commuting. There, I didn't think a lot about how my clothes fared in the weather -- it was either winter, and I threw a big coat on, or it was summer, and I was trying to wear as little as possible and be outside as little as possible. But in LA, people spend more of their day outside, all year long, so our regular wardrobes are adapted for it. Who needs sportier clothes for being outside at
Disneyland when we already spend all day walking around outside anyway?
As for wearing Disney stuff -- I don't really know! Maybe it has something to do with having more money to spend on merch in the parks since as locals we don't have to pay for airfare? FWIW I will also say that I see wayyyy more people walking around Los Angeles with Disney hats, shirts, scarves, sandals, bags, etc. than I ever have anywhere else. So possibly that's just a regional thing, too?