Tribe: Add class to list month header

functions.php

// add anywhere in functions.php theme file
add_filter( 'tribe_events_list_the_date_headers', 'add_class_to_month_header' );

function add_class_to_month_header( $content ) {
    $my_class = 'this-is-my-class';
    $content = str_replace( 'tribe-events-list-separator-month', 'tribe-events-list-separator-month ' . $my_class, $content );

    return $content;
}