You can look at analytic functions to avoid having to hit the second table twice. Something like this might work:
SELECT id AS col1, vid
FROM (
SELECT t1.id, t2.vid, RANK() OVER (PARTITION BY t1.id ORDER BY
CASE WHEN t2.startdte < TRUNC(SYSDATE) THEN t2.startdte ELSE null END
NULLS LAST) AS rn
FROM table1 t1
JOIN table2 t2 ON t2.id IN (t1.ID, t1.ID2)
)
WHERE rn = 1;
The inner select gets the id and vid values from the two tables with a simple join on id or id2. The rank function calculates a ranking for each matching row in the second table based on the startdte. It's complicated a bit by you wanting to filter on that date, so I've used a case to effectively ignore any dates today or later by changing the evaluated value to null, and in this instance that means the order by in the over clause needs nulls last so they're ignored.
I'd suggest you run the inner select on its own first - maybe with just a couple of id values for brevity - to see what its doing, and what ranks are being allocated.
The outer query is then just picking the top-ranked result for each id.
You may still get duplicates though; if table2 has more than one row for an id with the same startdte they'll get the same rank, but then you may have had that situation before. You may need to add more fields to the order by to break ties in a way that makes sens to you.
But this is largely speculation without being able to see where your existing query is actually slow.