I found the solution in this article:
https://www.advancedcustomfields.com/resources/creating-wp-archive-custom-field-filter/ .
I know that it causes a page refresh but going for Ajax based solution is an overkill.
This solution code is very elegant and easy to follow and understand.
Although taxonomy might be faster they require a lot of work with creating metaboxes and stuff so for small custom post type (Very few entries) there won’t be a performance penalty.
