Hi,
Thank you very much for the details, it helps us a lot.
I tried to test the plugin on the search results page, but it seems to work all right on our ends without logging in.
The most likely cause is the cache. If you are using a cache plugin, it might be serving yet outdated data and the plugin scripts might not be fetched yet. Make sure to clear all layers of cache – page, minify, asset, browser cache, CDN etc..
It will very likely resolve the issue 🙂