I seem to remember reading that adults can wear costumes in Galaxy's Edge but not the rest of the parks... which I'm not exactly sure how that would work, how you could change outfits between Galaxy's Edge and other locations. Maybe they're meaning that you can only wear costumes that you buy at Galaxy's Edge? Either way it would have to be within reason... No makes or helmets, no costumes that look like the ones cast members wear, and probably nothing with a name tag on it (which would make you look more like a cast member).
Disney is going to have to allow some kind of costuming, though, at least in Disney World. The Star Wars hotel will supposedly give you costumes to wear around Galaxy's Edge, so there's definitely some kind of wiggle room.
Personally, I'm planning to wear a costume of sorts, but one that could also be taken as just everyday wear. I'm thinking something like brown cargo pants, a gray shirt, brown sleeveless vest, brown shoes... Maybe with some Aurebesh writing on the back of the vest, a thin scarf around my neck, and a few greeblies here and there, a leather fanny pack... Nothing overtly "costume" but still something that fits in with the universe. I don't think something like that would be much of a problem.