I believe that ACF sets other values in $_POST for the taxonomy and the term id, but I am not sure. It should allow you to see if it’s a term page then alter the query to check terms instead of posts.
To see whats in $_POST during the ajax request you can do something like this
ob_start(); print_r($_POST); error_log(ob_get_clean());
This will print out the value of $_POST to your error log so you can inspect what’s in it.