It has to do with an added custom field. See:
Its a range and an option list.
Change the Field Input Type to Single Line Input Field
Now Search by Range is visible. Uncheck it.
Set the 'Field Input Type' back to the former value....
Ultimately, the answer was simply to enable "CiviCRM: access all custom data" for all users in Administer->Users & Permissions->Permissions->WordPress Access Control.
I am unclear whether this presents a data risk. The wording of the permission makes it feel a bit like this, but I guess if a user only has limited access by context then ...