Order WooCommerce products by Title, ignoring a leading "The"

gistfile1.txt

add_filter('posts_orderby', 'zbyte_edit_posts_orderby');

function zbyte_edit_posts_orderby($orderby_statement) {
	global $wp_query;

	$is_product_list = 
		is_shop() ||
		is_product_category() ||
		is_product_tag();

	if ( $is_product_list && $wp_query->get('orderby') == 'title' ) {
		$orderby_statement = "REPLACE(LOWER(wp_posts.post_title), 'the ', '') ASC";
	}

	return $orderby_statement;
}

Checking for the 'orderby' of 'title' should prevent this from running if the WooCommerce store admin has selected a different product ordering method from the default "Custom Ordering + name". A custom ordering will still override this. Remove the 'orderby' == 'title' check to make this override the sort on all product list pages.