Do BRIN indexes support ENUM types?
Aren't enums already ordered?


No.


  This commit, from 2014, implies that BRIN indexes should work for ENUM types.


That's actually not what that commit says. From the commit-message on the link you provided


  This type of operator class we call "Minmax", and we
  supply a bunch of them for most data types with B-tree opclasses.
  Since the BRIN code is generalized, other approaches are possible for
  things such as arrays, geometric types, ranges, etc; even for things
  such as enum types we could do something different than minmax with
  better results.  In this commit I only include minmax.


That doesn't mean it's there now. It is PostgreSQL for "patches accepted." In fact that commit explicitly says,

+/* no brin opclass for enum, tsvector, tsquery, jsonb, range */


Actually creating a BRIN index for an ENUM is, afaik, going to require some use of C and knowledge of index operator class implementation (pick/split/insert/merge).