Q:

MYSQL WHERE condition depends upon SELECT column

Is it possible to reference back to the column you're selecting in the WHERE condition?
I'm not even sure how to ask this question without excessive verbage, so I'll just try to point you to the "rated_user = @2User" part and note that @2User is what I'm selecting.
SELECT id, user, minimum 
INTO @1ID, @1User, @minimum 
FROM table1 
WHERE a_or_b = 'a' AND item = itemName 
ORDER BY number DESC LIMIT 1;

SELECT id, user 
INTO @2ID, @2User 
FROM table1 
WHERE a_or_b = 'b' AND item = itemName 
    AND (SELECT IFNULL(AVG(rating),0) AS Rating 
            FROM table2 
            WHERE rated_user = @2User AND completed = 'y'
        ) >= @minimum_seller_rating 
ORDER BY number ASC LIMIT 1;

A:

You should be able to just use the original column name from the parent table in the sub query as well. 
WHERE rated_user = user 

If there is a name collision, you may need to prefix it with the table name or alias.
WHERE rated_user = table1.user

