Here is an ugly solution (if you're desperate), it should work on 8.0 :
First create the t10 table that you'll use as an iterator (adjust it to your maximum array size):
CREATE TABLE T10 (ID INTEGER);
INSERT INTO T10 VALUES (1);
INSERT INTO T10 VALUES (2);
INSERT INTO T10 VALUES (3);
INSERT INTO T10 VALUES (4);
INSERT INTO T10 VALUES (5);
INSERT INTO T10 VALUES (6);
INSERT INTO T10 VALUES (7);
INSERT INTO T10 VALUES (8);
INSERT INTO T10 VALUES (9);
INSERT INTO T10 VALUES (10);
Then here is the test table :
create table table1 (
ids text[]
);
insert into table1 (ids) values (ARRAY['ID_two','ID_four']);
select * from table1;
ids
------------------
{ID_two,ID_four}
Then, the query, that use T10 to iterate over all members of your arrays :
\set myids ARRAY['''ID_one''','''ID_two''','''ID_three''']
select *
from (
select ids[iter.pos] as ids
from table1
join (select id as pos from t10) iter
on iter.pos <= array_length(ids,1)) as A
join (
select (:myids)[iter.pos] as ids
from (select id as pos from t10) iter
where iter.pos <= array_length(:myids,1)) as B
on a.ids = b.ids;
ids | ids
--------+--------
ID_two | ID_two