How on node forms do I set multiple vertical tabs to be always open? How can I make sure that the Menu Settings part when editing a node is always open just like the published section. See the image below.
You can do this with the hook_form_node_form_alter. Add the following to a custom module.

/**
 * Implements hook_form_FORM_ID_alter().
 */
function YourCustomModuleNAme_form_node_form_alter(&amp;$form, FormStateInterface $form_state){
  //- MENU SETTINGS
  $form["menu"]['#open']                 = TRUE;
  //- COMMENT SETTINGS
  $form["comment"]["widget"][0]['#open'] = TRUE;
}


Change the value of #open to true to show the menu as openend. 

In some cases it is necessary to move this hook implementation to the end of the list. Because the menu group added by menu_ui Module can overwrite your settings to #open false again. For this you can use the following: 

/**
 * Implements hook_module_implements_alter().
 */
function YourCustomModuleNAme_module_implements_alter(&amp;$implementations, $hook){
  switch ($hook) {
    // Move our hook_form_FORM_ID_alter() implementation to the end of the list.
    case 'form_alter':
      $group = $implementations['YourCustomModuleNAme'];
      unset($implementations['YourCustomModuleNAme']);
      $implementations['YourCustomModuleNAme'] = $group;
      break;
  }
}