SELECT a.CustomerId, a.CustomerName, a.UpdateDate, b.DateofBirth
FROM Table1 a
INNER JOIN (SELECT CustomerId, MAX(UpdateDate) as UDate
FROM Table1
GROUP BY CustomerId
) maxdate ON a.CustomerId = maxdate.CustomerId
AND a.UpdateDate = maxdate.UDate
INNER JOIN Table2 b ON a.CustomerId = b.CustomerId
Use SELECT DISTINCT se você tiver vários registros para um customerid e atualizado.