SQL Outer Join while conditioning on an extra column
You don't need subqueries. You only need to use both columns in the ON condition of the FULL JOIN:

SELECT
    -- t1.*,     -- adjust, keep only 
    -- t2.*,     -- needed columns
    COALESCE(t1.date, t2.date)
                  AS date, 
    COALESCE(t1.identifier, t2.identifier)
                  AS identifier, 
    t1.attribute1 AS a_attribute1,
    t1.attribute2 AS a_attribute2,
    t2.attribute1 AS b_attribute1,
    t2.attribute2 AS b_attribute2
FROM table1 AS t1 
     FULL JOIN table2 AS t2
     ON  t1. date = t2. date
     AND t1. identifier= t2. identifier
-- WHERE
--     (t1.date = '2000-01-01' OR t2.date = '2000-01-01')
 ;


If we want date and identifier combined in one column each, we can use COALESCE() function.