En lugar de 'omitir', simplemente configúrelo para que el valor no sea verdadero, usando NOT:
SELECT *
FROM posts p
JOIN relations r ON p.user_id = r.recipient
WHERE (r.status = 1 OR r.status = 2)
AND (r.sender = '$user_id' OR p.user_id = '$user_id')
AND NOT (r.status = 1 AND p.privacy = 2 AND p.user_id != '$user_id')
ORDER BY p.post_id DESC;"
