Ah I see! To clear up any confusion, when I say facets I mean the overarching field (i.e. Insurance AcceptedI) and when I say facet options I mean the individual options within it (i.e. Aetna, Cigna etc.)
But alas, today you cannot control the order of either of these things. What’s on the more immediate roadmap is to control the order of the facets. As you point out, you should be able to make Specialty appear first or Gender appear last. Important facets should be first; unimportant ones should go last.
Controlling the order of facet options is not something that is currently on the roadmap, but we would be interested to hear about the use case!