Update table using values from another table in SQL Server
There are quite a few ways to achieve your desired results.

Undeterministic methods

(in the event that many rows in table 2 match one in table 1)

UPDATE T1
SET    address = T2.address,
       phone2 = T2.phone
FROM   #Table1 T1
       JOIN #Table2 T2
         ON T1.gender = T2.gender
            AND T1.birthdate = T2.birthdate


Or a slightly more concise form

UPDATE #Table1
SET    address = #Table2.address,
       phone2 = #Table2.phone
FROM   #Table2
WHERE  #Table2.gender = #Table1.gender
       AND #Table2.birthdate = #Table1.birthdate 


Or with a CTE

WITH CTE
     AS (SELECT T1.address AS tgt_address,
                T1.phone2  AS tgt_phone,
                T2.address AS source_address,
                T2.phone   AS source_phone
         FROM   #Table1 T1
                INNER JOIN #Table2 T2
                  ON T1.gender = T2.gender
                     AND T1.birthdate = T2.birthdate)
UPDATE CTE
SET    tgt_address = source_address,
       tgt_phone = source_phone 


Deterministic methods

MERGE would throw an error rather than accept non deterministic results

MERGE #Table1 T1
USING #Table2 T2
ON T1.gender = T2.gender
   AND T1.birthdate = T2.birthdate
WHEN MATCHED THEN
  UPDATE SET address = T2.address,
             phone2 = T2.phone; 


Or you could pick a specific record if there is more than one match

With APPLY

UPDATE T1
SET    address = T2.address,
       phone2 = T2.phone
FROM   #Table1 T1
       CROSS APPLY (SELECT TOP 1 *
                    FROM   #Table2 T2
                    WHERE  T1.gender = T2.gender
                           AND T1.birthdate = T2.birthdate
                    ORDER  BY T2.PrimaryKey) T2 


.. Or a CTE

WITH T2
     AS (SELECT *,
                ROW_NUMBER() OVER (PARTITION BY gender, birthdate ORDER BY primarykey) AS RN
         FROM   #Table2)
UPDATE T1
SET    address = T2.address,
       phone2 = T2.phone
FROM   #Table1 T1
       JOIN T2
         ON T1.gender = T2.gender
            AND T1.birthdate = T2.birthdate
            AND T2.RN = 1;