add_action( 'pre_get_posts', 'wpk_set_main_query_orderby_random' );
function wpk_set_main_query_orderby_random( $query ) {
    if ( is_admin()
     || ! is_home()
     || ! $query->is_main_query()
     || ( isset( $_GET['orderby'] ) && $_GET['orderby'] !== 'date' )
    ) {
        return;
    }
    
    $query->set( 'orderby', 'rand' );
}