PostgreSQL: ОБНОВЛЕНИЕ подразумевает, преодолевают разделы

It can be made to work, the trigger that does the move just needs to be defined for each partition, not the whole table. So start as you did for table definitions and the INSERT trigger

CREATE TABLE records (
 record varchar(64) NOT NULL,
 active boolean default TRUE
);

CREATE TABLE active_records (CHECK (active)) INHERITS (records);
CREATE TABLE inactive_records (CHECK (NOT active)) INHERITS (records);

CREATE OR REPLACE FUNCTION record_insert()
RETURNS TRIGGER AS $$
BEGIN
  IF (TRUE = NEW.active) THEN
    INSERT INTO active_records VALUES (NEW.*);
  ELSE
    INSERT INTO inactive_records VALUES (NEW.*);
  END IF;
  RETURN NULL;
END;
$$
LANGUAGE plpgsql;

CREATE TRIGGER record_insert_trigger
 BEFORE INSERT ON records
 FOR EACH ROW EXECUTE PROCEDURE record_insert();

... let's have some test data ...

INSERT INTO records VALUES ('FirstLittlePiggy', TRUE);
INSERT INTO records VALUES ('SecondLittlePiggy', FALSE);
INSERT INTO records VALUES ('ThirdLittlePiggy', TRUE);
INSERT INTO records VALUES ('FourthLittlePiggy', FALSE);
INSERT INTO records VALUES ('FifthLittlePiggy', TRUE);

Now the triggers on the partitions. The if NEW.active = OLD.active check is implicit in checking the value of active since we know what's allowed to be in the table in the first place.

CREATE OR REPLACE FUNCTION active_partition_constraint()
  RETURNS TRIGGER AS $$
    BEGIN
      IF NOT (NEW.active) THEN
        INSERT INTO inactive_records VALUES (NEW.*);
        DELETE FROM active_records WHERE record = NEW.record;
        RETURN NULL;
      ELSE
        RETURN NEW;
      END IF;
    END;
    $$
    LANGUAGE plpgsql;

CREATE TRIGGER active_constraint_trigger
  BEFORE UPDATE ON active_records
  FOR EACH ROW EXECUTE PROCEDURE active_partition_constraint();

CREATE OR REPLACE FUNCTION inactive_partition_constraint()
  RETURNS TRIGGER AS $$
    BEGIN
      IF (NEW.active) THEN
        INSERT INTO active_records VALUES (NEW.*);
        DELETE FROM inactive_records WHERE record = NEW.record;
        RETURN NULL;
      ELSE
        RETURN NEW;
      END IF;
    END;
    $$
    LANGUAGE plpgsql;

CREATE TRIGGER inactive_constraint_trigger
  BEFORE UPDATE ON inactive_records 
  FOR EACH ROW EXECUTE PROCEDURE inactive_partition_constraint();

... and test the results ...

scratch=> SELECT * FROM active_records;
      record      | active 
------------------+--------
 FirstLittlePiggy | t
 ThirdLittlePiggy | t
 FifthLittlePiggy | t
(3 rows)

scratch=> UPDATE records SET active = FALSE WHERE record = 'ThirdLittlePiggy';
UPDATE 0
scratch=> SELECT * FROM active_records;
      record      | active 
------------------+--------
 FirstLittlePiggy | t
 FifthLittlePiggy | t
(2 rows)

scratch=> SELECT * FROM inactive_records;
      record       | active 
-------------------+--------
 SecondLittlePiggy | f
 FourthLittlePiggy | f
 ThirdLittlePiggy  | f
(3 rows)