How can I improve this nested MySQL query to avoid redundant WHERE statement?
Reformulating your query:

SELECT 
    numopens / numsends AS Open_Rate,
    numactions / numsends AS Action_Rate
FROM
    ( SELECT 
          ( SELECT COUNT(DISTINCT s.userID) 
            FROM tbl_sends AS s
            WHERE s.mailing_id = param.mailing_id
          )  
        AS numsends,
          ( SELECT COUNT(DISTINCT o.userID) 
            FROM tbl_opens AS o
            WHERE o.mailing_id = param.mailing_id
          )  
        AS numopens
          ( SELECT COUNT(DISTINCT a.userID) 
            FROM tbl_actions AS a 
            WHERE a.mailing_id = param.mailing_id
          )
        AS numactions
      FROM 
          ( SELECT 
                5694     AS mailing_id,
                417      AS another_parameter,
                'funny'  AS one_more_parameter   
          ) AS param  
    ) AS cte ;