WP Customizer Fatal Error trying to load class in child theme

I think that the error message is clear enough: the class was not found. The first thing you should do is to verify the path you are using to load the file where the class is defined.

If you do that and check the value of child_template_directory constant, you will see that it has not trailing slash, so this line:

load_template( child_template_directory . 'inc/customizer/class-my-customize-frontend.php' );

Should be:

load_template( child_template_directory . '/inc/customizer/class-my-customize-frontend.php' );

Anyway, there is a better way to get the child theme directoy path: get_stylesheet_directory() function.

I would do:

load_template( get_stylesheet_directory() . '/inc/customizer/class-my-customize-frontend.php' );

Or, at least I would define the constant in this way:

define('child_template_directory', get_stylesheet_directory() );

PD: Your porlbem It is not a WP Customizer Fatal Error.