Getting repeated value in a group_concat only if ids are different
First group by both activity_type and prod_id and then another group by activity_type:

SELECT 
    a.activity_type AS Activity, 
    COUNT(DISTINCT p.id) AS Products,
    CONVERT(GROUP_CONCAT(p.category_id SEPARATOR ',  ') USING utf8) 
      AS Categories
FROM 
    product AS p
  JOIN 
    ( SELECT activity_type
           , prod_id
      FROM activity 
      WHERE activity_type &lt;&gt; '' 
      GROUP BY activity_type
             , prod_id
    ) AS a
    ON p.id = a.prod_id
GROUP BY 
    activity_type
ORDER BY 
    Products DESC;


Tested in SQL-Fiddle (thank you @Mr.Radical)

You could also safely replace COUNT(DISTINCT p.id) with COUNT(*) in the above, as for every activity type, there are only distinct product IDs (this is taken care in the internal group by).