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.