Since you are just looking for 1 date, 12/13/1971, you could just write your SQL this way:

SELECT * FROM VOTER ;
WHERE tdob = to_date('12/31/1971', 'MM/DD/YYYY') ;
AND cvotstatus = 'A'

As for yuor observed performance difference, it is always better to use BETWEEN when a column value needs to be between 2 other values.