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;