Zoals opgemerkt in de opmerkingen, nam ik een aggregatiefunctie op, maar geen "groeperen op"-clausule.
Nu lijkt dit te werken (zojuist de GROUP BY . toegevoegd regel):
SELECT
p.id,
p.post_name,
c.name,
GROUP_CONCAT(t.`name`)
FROM wp_posts p
JOIN wp_term_relationships cr
on (p.`id`=cr.`object_id`)
JOIN wp_term_taxonomy ct
on (ct.`term_taxonomy_id`=cr.`term_taxonomy_id`
and ct.`taxonomy`='category')
JOIN wp_terms c on
(ct.`term_id`=c.`term_id`)
JOIN wp_term_relationships tr
on (p.`id`=tr.`object_id`)
JOIN wp_term_taxonomy tt
on (tt.`term_taxonomy_id`=tr.`term_taxonomy_id`
and tt.`taxonomy`='post_tag')
JOIN wp_terms t
on (tt.`term_id`=t.`term_id`)
GROUP BY p.id
+---------------+----------+----------------+
| post_id | category | tags |
|---------------+----------+----------------+
| 213 | news | tag1,tag2,tag3 |
+---------------+----------+----------------+
| 216 | whatever | tag2,tag3 |
+---------------+----------+----------------+
Bedankt Aardbei!