How can I drop and create postgresql views in dependency order?
You may take a look on "drop table base cascade". after that you have to recreace the structure on your own. I think its the easyer way. Or you can extend the answer, you found with some search in the pg_depend table.
For the "clean" method, please check the docs, as a dirty way here is a query:

WITH RECURSIVE t AS (
  SELECT c.oid,c.relname, 0 as level FROM pg_class c where relname='base' UNION ALL
  SELECT c.oid,c.relname, a.level+1 FROM t a
  JOIN pg_depend d ON d.refobjid=a.oid
  JOIN pg_rewrite w ON w.oid= d.objid AND w.ev_class!=a.oid
  JOIN pg_class c ON c.oid=w.ev_class
) SELECT distinct * FROM t order by level;