Ignoring initial articles (like ‘a’, ‘an’ or ‘the’) when sorting queries?

The Problem

I think there’s a typo in there:

The name of the filter is posts_fields not post_fields.

That could explain why the title2 field is unknown, because it’s definition isn’t added to the generated SQL string.

Alternative – Single filter

We can rewrite it to use only a single filter:

add_filter( 'posts_orderby', function( $orderby, \WP_Query $q )
{
    // Do nothing
    if( '_custom' !== $q->get( 'orderby' ) )
        return $orderby;

    global $wpdb;

    $matches="The";   // REGEXP is not case sensitive here

    // Custom ordering (SQL)
    return sprintf( 
        " 
        CASE 
            WHEN {$wpdb->posts}.post_title REGEXP( '^($matches)[[:space:]]+' )
                THEN TRIM( SUBSTR( {$wpdb->posts}.post_title FROM %d )) 
            ELSE {$wpdb->posts}.post_title 
        END %s
        ",
        strlen( $matches ) + 1,
        'ASC' === strtoupper( $q->get( 'order' ) ) ? 'ASC' : 'DESC'     
    );

}, 10, 2 );

where you can now activate the custom ordering with the _custom orderby parameter:

$args_post = array
    'post_type'      => 'release', 
    'orderby'        => '_custom',    // Activate the custom ordering 
    'order'          => 'ASC', 
    'posts_per_page' => -1, 
);

$loop = new WP_Query($args_post);

while ($loop->have_posts() ) : $loop->the_post();

Alternative – Recursive TRIM()

Let’s implement the recursive idea by Pascal Birchler, commented here:

add_filter( 'posts_orderby', function( $orderby, \WP_Query $q )
{
    if( '_custom' !== $q->get( 'orderby' ) )
        return $orderby;

    global $wpdb;

    // Adjust this to your needs:
    $matches = [ 'the ', 'an ', 'a ' ];

    return sprintf( 
        " %s %s ",
        wpse_sql( $matches, " LOWER( {$wpdb->posts}.post_title) " ),
        'ASC' === strtoupper( $q->get( 'order' ) ) ? 'ASC' : 'DESC'     
    );

}, 10, 2 );

where we can for example construct the recursive function as:

function wpse_sql( &$matches, $sql )
{
    if( empty( $matches ) || ! is_array( $matches ) )
        return $sql;

    $sql = sprintf( " TRIM( LEADING '%s' FROM ( %s ) ) ", $matches[0], $sql );
    array_shift( $matches );    
    return wpse_sql( $matches, $sql );
}

This means that

$matches = [ 'the ', 'an ', 'a ' ];
echo wpse_sql( $matches, " LOWER( {$wpdb->posts}.post_title) " );

will generate:

TRIM( LEADING 'a ' FROM ( 
    TRIM( LEADING 'an ' FROM ( 
        TRIM( LEADING 'the ' FROM ( 
            LOWER( wp_posts.post_title) 
        ) )
    ) )
) )

Alternative – MariaDB

In general I like to use MariaDB instead of MySQL. Then it’s much easier because MariaDB 10.0.5 supports REGEXP_REPLACE:

/**
 * Ignore (the,an,a) in post title ordering
 *
 * @uses MariaDB 10.0.5+
 */
add_filter( 'posts_orderby', function( $orderby, \WP_Query $q )
{
    if( '_custom' !== $q->get( 'orderby' ) )
        return $orderby;

    global $wpdb;
    return sprintf( 
        " REGEXP_REPLACE( {$wpdb->posts}.post_title, '^(the|a|an)[[:space:]]+', '' ) %s",
        'ASC' === strtoupper( $q->get( 'order' ) ) ? 'ASC' : 'DESC'     
    );
}, 10, 2 );