Thanks!
The cache does not seem to clear at all. I tried to add exclusions to the inline scripts section as well, but it has no effect. I also tried to remove the plugin script from the exclusions, but it is still there on the front-end.
Adding these lines to the inline scripts exlusions box should probably help:
wpdreams
ajaxsearchproHowever there is a disclaimer in the WP rocket back-end as well, that he script combination can actually break things. Looks like that feature might be problematic in general.