Sql LEFT OUTER JOIN with WHERE clause

Move the constraint to your on clause.

select *
from request r
left join requestStatus rs
on r.requestID = rs.requestID
--and status_id = 1
and status_id <> 2

What's happening to you is that the outer join is performed first. Any rows coming from the outer join that don't have matches will have nulls in all the columns. Then your where clause is applied, but since 1 <> null, it's not going to work like you want it to.

EDIT: Changed on clause based on Piyush's comment.

In SQL Server 2017 you can put AND after ON in this way

SELECT * FROM Request
LEFT OUTER JOIN RequestStatus ON Request.RequestID = RequestStatus.RequestID
AND RequestStatus.StatusID <> 2
WHERE Request.RequestID IS NOT NULL