virk Oh, wow, thank you for kindly checking. So then there is not a problem with the fastwiki plugin.
I did have indexmenu, but I hardly use it so I removed it. Still have the issue, unfortunately. (I tried ?purge to force the page to recache https://www.dokuwiki.org/devel:caching#purging_the_cache)
https://animecards.org/doku.php?id=list7:soul_eater << this page will allow me to inline edit, but I noticed that when I click the edit button, the box does appear just before the edit field shows up. I couldn't tell you if it always did that. Did you notice something like that when you used it? If you didn't have it, then perhaps it is a sitewide issue.
From the configuration menu, these are the plugins I have (at least, the plugins that have configuration options):
Blog
Captcha
Catlist
Cloud
Datatables
Edittable
Emphasis
Fastwiki
Folded
Gallery
Imagebox
Imagecarousel
Include
Medialist
Move
Pageimage
Pagelist
Snippeter
Stars2
Tablelayout
Tag
Tagfilter
Translation
Twitter
Vshare
Wrap
Are there likely suspects above? I know andi mentioned image gallery. Some I am pretty reliant on... I'm completely open to doing a fresh install in case it is some truly random thing. I can also do a test install.