Create a composite index either on postings (is_active, post_date) (in that order).
It will be used both for filtering on is_active and ordering by post_date.
MySQL should show REF access method over this index in EXPLAIN EXTENDED.
Note that you have a RANGE filtering condition over user_offtopic_count, that’s why you cannot use an index over this field both in filtering and in sorting by other field.
Depending on how selective is your user_offtopic_count (i. e. how many rows satisfy user_offtopic_count < 10), it may be more useful to create an index on user_offtopic_count and let the post_dates be sorted.
To do this, create a composite index on postings (is_active, user_offtopic_count) and make sure the RANGE access method over this index is used.
Which index will be faster depends on your data distribuion. Create both indexes, FORCE them and see which is faster:
CREATE INDEX ix_active_offtopic ON postings (is_active, user_offtopic_count);
CREATE INDEX ix_active_date ON postings (is_active, post_date);
SELECT
`postings`.`id`,
UNIX_TIMESTAMP(postings.post_date) as post_date,
`postings`.`link`,
`postings`.`title`,
`postings`.`author`,
`postings`.`excerpt`,
`postings`.`long_excerpt`,
`feeds`.`title` AS feed_title,
`feeds`.`website` AS feed_website
FROM
`postings` FORCE INDEX (ix_active_offtopic)
JOIN
`feeds`
ON
`feeds`.`id` = `postings`.`feed_id`
WHERE
`feeds`.`type` = 1 AND
`postings`.`user_offtopic_count` < 10 AND
`postings`.`is_active` = 1
ORDER BY
`postings`.`post_date` desc
LIMIT
15
/* This should show RANGE access with few rows and keep the FILESORT */
SELECT
`postings`.`id`,
UNIX_TIMESTAMP(postings.post_date) as post_date,
`postings`.`link`,
`postings`.`title`,
`postings`.`author`,
`postings`.`excerpt`,
`postings`.`long_excerpt`,
`feeds`.`title` AS feed_title,
`feeds`.`website` AS feed_website
FROM
`postings` FORCE INDEX (ix_active_date)
JOIN
`feeds`
ON
`feeds`.`id` = `postings`.`feed_id`
WHERE
`feeds`.`type` = 1 AND
`postings`.`user_offtopic_count` < 10 AND
`postings`.`is_active` = 1
ORDER BY
`postings`.`post_date` desc
LIMIT
15
/* This should show REF access with lots of rows and no FILESORT */