That plugin, and others like it, will impact sorting in our plugin as it acts later in the WordPress page creation process. Post Types Order does have a hook you can use though, to stop it working under conditions that you set. It is discussed here:
https://wordpress.org/support/topic/to-avoid-plugin-conflict-how-to-disable-post-type-order-for-search-pages/
Maybe like this (in your child theme functions.php file):
add_filter('pto/posts_orderby/ignore', 'pto_ignore', 10, 3);
function pto_ignore( $ignore, $orderBy, $query ) {
global $searchandfilter;
$sf_current_query = $searchandfilter->get(12345)->current_query();
if ((!$sf_current_query->is_filtered())&&($sf_current_query->get_search_term()=="")) {
} else {
$ignore = TRUE;
}
return $ignore;
}
Where 12345 is changed to the ID of your search?
I am not sure if this is much the same, but simpler/shorter:
add_filter('pto/posts_orderby/ignore', 'pto_ignore', 10, 3);
function pto_ignore( $ignore, $orderBy, $query ) {
global $searchandfilter;
$sf_current_query = $searchandfilter->get(12345)->current_query();
if (!((!$sf_current_query->is_filtered())&&($sf_current_query->get_search_term()==""))) $ignore = TRUE;
return $ignore;
}