I’m also seeing this behavior. Filter fields are hidden for Relationship, Page Link, Post Object, and User field types. The Taxonomy field type displays the filters as expected.
i’m currently going through this process with wpengine right now. while it’s really strange that they’re aggressively caching wp-admin, there’s likely a reason why it makes sense for them and the workaround is just to disable it while you’re working on a site. what baffles me, however, is that they’re caching wp-admin for staging sites as well. yikes.
i worked on a site last fall and made extensive use of acf and the flexible content add-on…didn’t experience these issues at all. i wonder what’s changed?