After almost tearing my hair out while trying to get those two to fully work together, I found the solution in the end. While most of the things that can be read here and there are right and true, all solutions I found one the web have one problem: After activating nice URLs in Dokuwiki, you won’t be able to use ACLs anymore with Nginx as the web front end.
The solution is quite simple, there’s an additional global rewrite needed:
The reason being that if you rely on “try_files” doing the right thing, it will do what you want for normal pages. But it will trigger a 302 redirect for admin pages, thereby losing all the POST data that should have been sent. Using the rewrite will keep the POST data and thus make the ACLs editing work again, even with pretty URLs.