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[Waiting for user confirmation]Parent and Child Select boxes based on taxonomies
The only I see is to write a custom code. GEO my WP uses WP’s built in function wp_dropdown_categories to display the dropdowns. You will need to manually pull the taxonomies terms from database and run a loop to create something similar to the demo that you linked above.
Sorry I cannot be more helpful but I don’t see any other way it can be done.