A simple script demonstrating PostgreSQL idempotent capabilities. You can run this script as many times as you wish (it will not give duplicate object error or similar).

idempotent_script.sql

--Table
CREATE TABLE IF NOT EXISTS person (
  id integer NOT NULL,
  person_name character varying(40) NOT NULL,
  updated_date date,
  CONSTRAINT person_pkey PRIMARY KEY (id)
);
  
--Index
CREATE INDEX IF NOT EXISTS idx_person_name ON person (person_name);
 
--Sequence
CREATE SEQUENCE IF NOT EXISTS seq_person_inc;

--Function
CREATE OR REPLACE FUNCTION simple_sum(a_integer int, b_integer int) RETURNS INT
    AS $$ SELECT a_integer+b_integer $$
LANGUAGE SQL;
 
--View
CREATE OR REPLACE VIEW vw_select_1 AS
    SELECT 1;
  
--Role
DO $$
BEGIN
    CREATE ROLE rick_deckard;    
EXCEPTION   
    WHEN duplicate_object THEN
        RAISE NOTICE 'Role already exists. Ignoring...';    
END$$;

--Simple insert
INSERT INTO person (id, person_name) VALUES (1, 'HAL-9000'); 
 
--Upsert (insert + update)
INSERT INTO person (id, person_name) VALUES (1, 'Betrayer') ON CONFLICT ON CONSTRAINT person_pkey DO UPDATE SET person_name = EXCLUDED.person_name;
  
--Upsert (ignoring duplicate error)
INSERT INTO person (id, person_name) VALUES (1, 'HAL-9000') ON CONFLICT ON CONSTRAINT person_pkey DO NOTHING;
 
--Upsert (ignoring any error)
INSERT INTO person (id, person_name) VALUES (1, 'HAL-9000') ON CONFLICT DO NOTHING;
 
--Field
DO $$
BEGIN
    ALTER TABLE person ADD COLUMN id_another_person INTEGER;
EXCEPTION   
    WHEN duplicate_column THEN
        RAISE NOTICE 'Field already exists. Ignoring...';
END$$;
 
--Constraint
DO $$
BEGIN
    ALTER TABLE person ADD CONSTRAINT person_id_another_person_fkey FOREIGN KEY (id_another_person) REFERENCES person (id);
EXCEPTION   
    WHEN duplicate_object THEN
        RAISE NOTICE 'Constraint already exists. Ignoring...';
END$$;
 
--Trigger
CREATE OR REPLACE FUNCTION person_trigger_function() RETURNS trigger AS $BODY$
BEGIN
   --Something complex here =)
   RETURN NEW; 
END;
$BODY$
LANGUAGE plpgsql;
 
DO $$
BEGIN
    CREATE TRIGGER person_trigger BEFORE INSERT OR UPDATE ON person FOR EACH ROW EXECUTE PROCEDURE person_trigger_function();
EXCEPTION   
    WHEN duplicate_object THEN
        RAISE NOTICE 'Trigger already exists. Ignoring...';
END$$;

--Drop
DROP TRIGGER IF EXISTS person_trigger ON person;
DROP INDEX IF EXISTS idx_person_name;
ALTER TABLE person DROP COLUMN IF EXISTS person_name;
ALTER TABLE person DROP CONSTRAINT IF EXISTS person_id_another_person_fkey;
DROP ROLE IF EXISTS rick_deckard;
DROP VIEW IF EXISTS vw_select_1;
DROP FUNCTION IF EXISTS simple_sum(integer, integer);
DROP FUNCTION IF EXISTS person_trigger_function();
DROP TABLE IF EXISTS person;
DROP SEQUENCE IF EXISTS seq_person_inc;

If you ADD CONSTRAINT … PRIMARY KEY on a table that already has a primary key, you get back ERROR: multiple primary keys for table "campaign_results_exports" are not allowed, which is exception invalid_table_definition, so it doesn't trigger the WHEN duplicate_object block.

So the idempotent way to add primary key constraints, I think, is:

--Constraint (primary key)
DO $$
BEGIN
    ALTER TABLE person ADD CONSTRAINT person_pkey PRIMARY KEY (id);
EXCEPTION   
    WHEN invalid_table_definition THEN
        RAISE NOTICE 'Primary key already exists. Ignoring...';
END$$;

And how about idempotency while creating a database?