Success! I’ve discovered that the problem is to do with how CF caches requests when the CF proxy is enabled. All of my XWiki, Tomcat, and Nginx config was correct. I don’t know what caused the CF cache to become corrupt, or why that corruption only effected Firefox, but I used the “Purge Everything” option and XWiki immediately started working as expected in Firefox. I even set edit.document.inPlaceEditing.enabled back to true and in place editing is working again.
I suspect that whatever corrupted the CF cache in the first place will happen again, and if it does I will either create a CF “Cache Rule” which disables caching for my XWiki subdomain, or add a cache-control header to the request in the Nginx config, something like add_header Cache-Control "private, no-store, no-cache, must-revalidate";