PL/PgSQL function shuffles all values in a column. A table must have unique 'id' field.

shuffle_function.sql

CREATE OR REPLACE FUNCTION shuffle(table_name TEXT, field_name TEXT) RETURNS void AS $$
DECLARE entry RECORD;
DECLARE entry_to_swap RECORD;

BEGIN 	
	FOR entry IN execute format('select * from %s', table_name) LOOP
		drop table if exists tmp_entry_to_swap;
		execute format('create temp table tmp_entry_to_swap as (select * from %s order by random() limit 1)', table_name);

		select * into entry_to_swap from tmp_entry_to_swap;
		
		if entry.id <> entry_to_swap.id then
			execute format(
				'UPDATE %1$s dst set %2$s = src.%2$s
				FROM %1$s src
				WHERE dst.id IN (' || entry.id || ', ' || entry_to_swap.id || ')
				AND src.id in (' || entry.id || ', ' || entry_to_swap.id || ') AND dst.id <> src.id', table_name, field_name
			);
		end if;
	END LOOP;
END;	
$$ LANGUAGE plpgsql;