I normally think of a churro as a kind of eat-as-you-walk snack, as opposed to something served alongside ice cream and covered in chocolate and whipped cream.
I've made them savory before, pretty good with some Parmesan and dipped in tomato sauce, or stuffed with cheese and mushroom pâté.
Other sweet things that are good savory are waffles, leftover grilled corn topped with crema, chillies, and lime juice. And French toast, I'm partial to just throwing some Garam Masala in the batter, then topping with chutney, or tamarind sauce.
Yes, that's Chinese. I love them and they're pretty easy to make. It's a laminated dough, but much more forgiving than a croissant which can be a biznatch to make in a hot kitchen.