Declaring an instance of class included in parent theme from child theme functions.php

Handle all the class loading in your parent theme on a predictable action (point in time) and hook in later in your child theme.

Example:

add_action( 'wp_loaded', 'parent_prefix_load_classes', 10 );

function parent_prefix_load_classes()
{
    $classes = [ 'Extra_Comment_Walker', 'Extra_Nav_Menu_Walker' ];

    foreach ( $classes as $class )
    {
        locate_template( "php/class.$class.php", TRUE, TRUE );
    }
}

Create instances in your child theme make sure your code runs after the classes are loaded:

// Priority 11 to run after the parent theme's loader.
add_action( 'wp_loaded', 'child_prefix_create_objects', 11 );

function child_prefix_create_objects()
{
    $nav_walker = new Extra_Nav_Menu_Walker;
}

Rules of thumb:

• Never load anything just when the file (function.php) is called. Wait for wp_loaded.
• Use the priority argument to control the order of execution.

Some notes:

• Custom post types, taxonomies and shortcodes belong to plugins. They should never be part of a theme, because that would create a lock-in effect for the user. If a theme switch would break the content you did something wrong.
• Do not use require_once in a theme. locate_template() is more flexible. You can overwrite the whole class now in your in child theme if you use the same directory structure.