Modify Genesis Custom Header CSS

Hook onto the same action as the genesis header function and kick out your overriding CSS:

function wpse_218701_genesis_header() {
    ?>

<style>
    body.custom-header #header {
        background-color: white !important;
    }
</style>

<?php
}

add_action( 'genesis_header', 'wpse_218701_genesis_header' );