I'm way, WAY out of my depth with this question, but curiosity got the better of me.
Anyway.
I've heard that $0$-categories are basically just sets. This seems wrong to me, since sets are kind of like "skeletal" setoids. Thus, since we don't assume every $1$-category is skeletal, similarly I don't think we should assume that every $0$-category is a set.
So, are $0$-categories best viewed as sets, or setoids?
Please keep answers as non-technical as possible, since I know absolutely nothing about the subject matter.
When talking about categories, one often considers that things that aren't preserved by equivalence are things that don't really matter to begin with.
Even without appealing to the category theoretic point of view, one might claim that ordinary sets are best viewed as setoids. To wit, many of the sets one deals with in practice are presented as quotient sets. For example, when doing with modular arithmetic, it is (IMO) somewhat more convenient to work with integers modulo an equivalence relation, rather than working with equivalence classes or reduced representatives.