Something else I forgot to mention is that I added ‘post’ to the Custom Rewrite Slug field. I then realized that this was a mistake too, so I removed it again.
When I look at the database tables of the posts, in the column GUID I can see several different links. Some are formatted as /dier/felix, some as /post/dobey, but all belong to CPT ‘dier’.
Even changing the permalink structure in WP to default, links like domain.com/?dier=felix don’t work.