Necesita un alias para la subconsulta y debe aplicar las condiciones a las dos consultas que une:
SELECT MAX(DateTime)
FROM (
SELECT DateTime
FROM Class_Searches
WHERE User_Email = '[email protected]'
AND DateTime > NOW( ) - INTERVAL 30 DAY
UNION ALL
SELECT DateTime
FROM Book_Searches
WHERE User_Email = '[email protected]'
AND DateTime > NOW( ) - INTERVAL 30 DAY
) AS x
o devolver datos para que pueda aplicar la condición en la consulta externa:
SELECT MAX(DateTime)
FROM (
SELECT DateTime, User_Email
FROM Class_Searches
UNION ALL
SELECT DateTime, User_Email
FROM Book_Searches
) AS x
WHERE User_Email = '[email protected]'
AND DateTime > NOW( ) - INTERVAL 30 DAY