Operator does not exist: json = json
In short - use JSONB instead of JSON or cast JSON to JSONB.
You cannot compare json values. You can compare text values instead:
SELECT * FROM movie_test WHERE tags::text = '["dramatic","women","political"]'
Note however that values of type JSON are stored as text in a format in which they are given. Thus the result of comparison depends on whether you consistently apply the same format:
SELECT '["dramatic" ,"women", "political"]'::json::text = '["dramatic","women","political"]'::json::text -- yields false!
In Postgres 9.4+ you can solve this problem using type JSONB, which is stored in a decomposed binary format. Values of this type can be compared:
SELECT '["dramatic" ,"women", "political"]'::jsonb = '["dramatic","women","political"]'::jsonb -- yields true
so this query is much more reliable:
SELECT * FROM movie_test WHERE tags::jsonb = '["dramatic","women","political"]'::jsonb
Read more about JSON Types.