Weekdays as terms – How to order taxonomy terms by ID in admin panel?

Method #1 – Modifying the query arguments

If we want to modify the term order for the schedule_day_taxonomy term checklist, on the single schedule cpt edit screen, then we can use the following setup:

add_action( 'load-post.php', function()
{
    add_filter( 'wp_terms_checklist_args', 'wpse_terms_checklist_args' );
} );

function wpse_terms_checklist_args( $args )
{         
    // Target the 'schedule' custom post type edit screen
    if( 'schedule' === get_current_screen()->id )
        add_filter( 'get_terms_args', 'wpse_terms_args', 10, 2 );
    return $args;
}

function wpse_terms_args( $args, $taxonomies )
{
    // Target the 'all' tab in the 'schedule_day_taxonomy' terms check list 
    if(
           isset( $args['get'] )
        && 'all' === $args['get']
        &&  isset( $taxonomies[0] )
        && 'schedule_day_taxonomy' === $taxonomies[0]
    ) {
        // Modify the term order
        $args['orderby'] = 'ID';  // <-- Adjust this to your needs!
        $args['order']   = 'ASC'; // <-- Adjust this to your needs!

        // House cleaning - Remove the filter callbacks
        remove_filter( current_filter(), __FUNCTION__ );        
        remove_filter( 'wp_terms_checklist_args', 'wpse_terms_checklist_args' );
    }
    return $args;
}

Another possibility would be to combine this into a single get_terms_args filter callback.

To get the following day order:

Sun, Mon, Tue, Wed, Thu, Fri, Sat

we could modify the corresponding term slugs and use:

// Modify the term order
$args['orderby'] = 'slug';  
$args['order']   = 'ASC'; 

Method #2 – Re-ordering the query results

If we don’t want to modify the slug, then here’s another approach.

We can re-order the resulting terms array, in the same order as the localized weekdays.

add_filter( 'wp_terms_checklist_args', function( $args )
{         
    add_filter( 'get_terms', 'wpse_get_terms', 10, 3 );
    return $args;
} );

function wpse_get_terms( $terms, $taxonomies, $args )
{
    if(     isset( $taxonomies[0] )
        && 'schedule_day_taxonomy' === $taxonomies[0]
        && 'schedule' === get_current_screen()->id
    ) {
        $newterms = [];
        foreach( (array) $GLOBALS['wp_locale']->weekday as $day )
        {
            foreach( (array) $terms as $term )
            {
                if( $term->name === $day )
                    $newterms[] = $term;
            }
        }
        remove_filter( current_filter(), __FUNCTION__ );
        if( 7 === count( $newterms ) )
            $terms = $newterms;
    }
    return $terms;
}

We could also replace

$GLOBALS['wp_locale']->weekday

with a custom weekdays array, ordered in a custom way.

Here’s the English version:

and here’s the Icelandic version:

Method #3 – Custom SQL ordering

We could modify the SQL ordering with the get_terms_orderby filter, with a CASE/WHEN/THEN setup.

Hopefully you can adjust this to your needs.