I guess because of the latest security fix “Added a few security measures for back-end ajax handlers as well as some page forms” with the latest version we aren’t able to search for taxonomy items in “Frontend Search Settings → Categories and Taxonomy Terms → Change display mode” anymore.
Indeed, I can confirm this is a new bug. I have noted it to the issue tracker.
Until then, you can fix it manually if you want to by:
– Opening up the wp-content\plugins\ajax-search-pro\backend\settings\assets\types.js file on your server
– Replacing it’s contents with this
– Saving
– Clearing the browser and site/CDN cache and reloading