Create result set with all records from LEFT table, and from the RIGHT table only bring records that do no exist in left already
Assuming all the columns are compatible:

SELECT * from table1
UNION ALL
SELECT table2.* from table2 left join table1 using (customer_id, date)
    where table1.customer_id is null


If not all the columns are compatible, you will have to do a bit of tedious manipulation of the select lists, rather than using *.