My workaround to this problem:
I set a custom link pointing to “index.php” without https://
then I’m using a bit of jQuery to add the right class to the right menu item when the visitor is on the home page:
<?php if ( is_home() || is_front_page() ): ?>
<script>$('#menu-id li:first').addClass('current-menu-item');</script>
<?php endif; ?>