Found the solution:
In rss.php is a part that checks the rights of a group:
$result = $db->query("
SELECT p.id AS id, p.message AS message, p.posted AS postposted, t.subject AS subject, f.forum_name, c.cat_name
FROM ".$db->prefix."posts p
LEFT JOIN ".$db->prefix."topics t
ON p.topic_id=t.id
INNER JOIN ".$db->prefix."forums AS f
ON f.id=t.forum_id
LEFT JOIN ".$db->prefix."categories AS c
ON f.cat_id = c.id
LEFT JOIN ".$db->prefix."forum_perms AS fp
ON (
fp.forum_id=f.id
AND fp.group_id=4
)
WHERE (
fp.read_forum IS NULL
OR fp.read_forum=1
)
Important in this piece of code is:
If this group ID is wrong or it is the code of the group with different rights then it doesn't work like it should. For people who made up groups by themselves it's a good thing to know!