SELECT
t.[column1],
pr.[RespondedDttm] as LastRespondedDate,
t.[column2],
t.[column3],
t.[column4]
FROM
Table1 t
LEFT JOIN
(
SELECT
t2.[Column1]
,t2.[column2]
,[RespondedDttm]
,RowNum = ROW_NUMBER() OVER (PARTITION BY ColWithDups ORDER BY [RespondedDttm])
,WithTiesRowNum = RANK() OVER (PARTITION BY ORDER BY [RespondedDttm] DESC)
FROM
Table2 t2
WHERE
t2.[RespondedDttm] >= '2015-09-01'
AND t2.[Response] IS NOT Null
) pr
ON (t.[column1] = pr.[column1])
AND pr.RowNum = 1
--AND pr.WithTiesRowNum = 1 --use this line if you want ties
WHERE
t.[column8] IN (value)
You can use window functions and ROW_NUMBER if you want only 1 row or RANK() if you want all ties.
In case you wanted the other direction of the nuance which I think you comment suggests:
SELECT
t.[column1],
pr.[RespondedDttm] as LastRespondedDate,
t.[column2],
t.[column3],
t.[column4]
FROM
Table1 t
LEFT JOIN
(
SELECT
t2.[Column1]
,t2.[column2]
,[RespondedDttm]
,RowNum = ROW_NUMBER() OVER (PARTITION BY ColWithDups ORDER BY [RespondedDttm])
,WithTiesRowNum = RANK() OVER (PARTITION BY ORDER BY [RespondedDttm] DESC)
FROM
Table2 t2
) pr
ON (t.[column1] = pr.[column1])
AND pr.[RespondedDttm] >= '2015-09-01'
AND pr.[Response] IS NOT Null
AND pr.RowNum = 1
--AND pr.WithTiesRowNum = 1 --use this line if you want ties
WHERE
t.[column8] IN (value)