SELECT FOR UPDATE locking other tables in PostgreSQL
We also don't ever update primary keys.

In that case, I think you can use FOR NO KEY UPDATE instead of FOR UPDATE. It's a weaker lock, as explained in Postgres docs about Explicit Locking:

FOR NO KEY UPDATE
Behaves similarly to FOR UPDATE, except that the lock acquired is weaker: this lock will not block SELECT FOR KEY SHARE commands that attempt to acquire a lock on the same rows. This lock mode is also acquired by any UPDATE that does not acquire a FOR UPDATE lock.

Test:
-- Setup
create table a (id int primary key, 
                x varchar);
create table b (id int primary key 
                    references a (id) on update cascade on delete cascade, 
                x varchar);
insert into a values (1), (2);
insert into b values (1, null), (2, null);

-- Left
begin;
select 1 from a for no key update;
/* Keep the transaction open */

            -- Right
            begin;
            update b set x = 'abc' where id = 1;
            update b set x = 'xyz';    -- doesn't block

-- Left
update a set x = 'left' where id = 1;
commit ;

            -- Right
            commit ;