I think I understand now, I saw those filters but could not find the particular terms you mentioned so I was not sure it's the one.
Now, whatever you want to hide on the site, depending on what was chosen in the Filter, can only be done by listening to the URL parameters of that filter.
Let's say, I click on the filter to filter by any Taxonomy Term
This will generate some new URL (either by AJAX or not) that reflects this query.
This ONLY works if you show the search terms in the URL, and it seems you are using the AJAX updated and URL hidden method.
Hence, that won't work with the usual methods, and even if you show the Search query in the URL, you can hide only partials of your search.
In that case, you can listen to the ShortCode wpv-search-term and if it is the value you check upon either hide or show entire Filters with HTML conditionals.
It is NOT possible to hide SINGLE items of a Select of the same filter, depending on what was selected.
This is only possible if you hide "empty" items, means, if selection A would return no results in selection B then that option would be possible to be removed or disabled.
That, is only WITHIN the same filter, while HTML conditions are for a whole set of a filter (for example, to hide an entire Category filter, but not just single options of it)
As you see, it will be complex.
Can you precisely elaborate to me, in that filter on the left side, what exact sections or terms you would have to be removed when?
The example of hiding an entire section with HTML conditional when a certain search is run:
[wpv-conditional if="( '[wpv-search-term param='url_param_you_listen_to']' eq 'what you search for' )"]
put the search section to hide in here
[/wpv-conditional]
Above will show "put the search section to hide in here" only if you search for "what you search for" in the filter "url_param_you_listen_to".
Please let me know if this would help, but it hides only entire sections, not single options.
Single options, as said, can be hidden only for single searches, when you "Let me choose individual settings manually", and then "Show only available options for each input", in the Custom Search Settings.