Error from Impala-
all DISTINCT aggregate functions need to have the same set of parameters as count(DISTINCT (CASE WHEN (secondcol >= 0) THEN 1 ELSE CAST(NULL AS STRING) END))
deviating function: count(DISTINCT (CASE WHEN (secondcol >= 0) THEN 1 ELSE NULL END))

Query:
SELECT user_key, sum(firstcol),count(distinct case when secondcol >= 0 then 1 end)
FROM sometable
WHERE customer_key=6
GROUP BY user_key
HAVING sum(firstcol)>100
AND count(distinct case when secondcol >= 0 then 1 end)=0

Query explanation:
For all users
Add up values in the firstcol column (integer column)
count distinct values in secondcol where secondcol value zero or more
otherwise return null (output is string)

Translated Teiid query:
SELECT user_key, SUM(firstcol) as `EXPR_0`, COUNT(DISTINCT (CASE WHEN (secondcol >= 0) THEN '1' ELSE CAST(NULL AS STRING) END)) as `EXPR_1`
FROM sometable
WHERE customer_key` = 6
HAVING (EXPR_0 > 100) AND (COUNT(DISTINCT (CASE WHEN (secondcol >= 0) THEN '1' ELSE NULL END)) = 0))

Note the difference between the select and having for EXPR_1:
Select - THEN '1' ELSE CAST(NULL AS STRING) END
Having - THEN '1' ELSE NULL END

Impala doesn't accept that these are the same aggregate function. Aliases aren't accepted in the HAVING.

One further observation- if we swap the translation and write the statement in the select as
COUNT(DISTINCT (CASE WHEN (secondcol >= 0) THEN '1' ELSE NULL END))

Teiid translates the SELECT to
COUNT(DISTINCT (CASE WHEN (secondcol >= 0) THEN '1' ELSE CAST(NULL AS STRING) END))

So it always makes these mismatched.