Settings not working when not login WordPress

Hi hrvojeos,
this is almost certainly caused because you are caching the page. The fact that when you are logged in it works is evidence of this since most caching plugins will not show cached pages for logged in users.

Taking a look at your page (thanks for the link!) it looks like HD Quiz itself is properly working and loading, but your site is not loading the CSS stylesheet.

I recommend the following.

1. Clear your site cache. https://docs.wp-rocket.me/article/53-clear-wp-rocket-cache
   This will allow WP Rocket to rebuild your cache, hopfuly error free this time
2. If rebuilding the cache does not help, exclude the page from being cached. https://docs.wp-rocket.me/article/54-exclude-pages-from-the-cache
3. If you absolutely want to keep caching enabled on that page, you can try excluding the style sheet only

NOTE: I see that on your site, you are not actually loading any style sheets at all, and are loading everything inline. On most sites, this is a very bad idea and is almost certainly making your site slower instead of faster. You might want to disable that feature in WP Rocket

EDIT: You beat me to it. Glad you got it working!