How can I skip the current password validation on the user form?
A working code example for this is the No Current Password module.
Here's the relevant code:

/**
 * Implements hook_form_FORM_ID_alter().
 * Remove the current password field from the user_profile_form form (user/%/edit).
 */
function nocurrent_pass_form_user_form_alter(&amp;$form, &amp;$form_state) {

  // Get the module's configuration
  $config = \Drupal::config('nocurrent_pass.settings');
  $nocurrent_pass_disabled = $config-&gt;get('nocurrent_pass_disabled');

  // If the Current password is disabled
  if ($nocurrent_pass_disabled) {

    $account = \Drupal::service('current_route_match')-&gt;getParameter('user');

    // If this is not the Superadmin's edit page
    if ( !empty($account) &amp;&amp; ($account-&gt;id() != 1) ) {

      // Turn off Current password field's validation
      $form_state-&gt;set('user_pass_reset', 1);

      // Hide the Current password fields
      $form['account']['current_pass']['#access'] = FALSE;
    }
  }
}