Problem:

How can two views, both on the same page, both use the same query filter with same URL parameter?

Solution:

Yes, it is possible to pass same URL parameter to both views, and take effect on both of them, you can disable AJAX search, for example:

Edit both post views:

1) in section "Custom Search Settings", enable option: Full page refresh when visitors click on the search button,

2) In section "Search and Pagination", add a submit button

Relevant Documentation: