Drupal 8 code to mark as active all the menu links poiting to /user when viewing an user's own profile.

MODULE.module

/**
 * Implements hook_preprocess_HOOK().
 *
 * @note: This can be removed if https://www.drupal.org/project/drupal/issues/2870054 is fixed.
 */
function MODULE_preprocess_menu(&$variables) {

  /** @var Drupal\Core\Routing\CurrentRouteMatch */
  $routeMatcher = \Drupal::routeMatch();
  /** @var Drupal\Core\Routing\RouteMatch */
  $currentRouteMatch = $routeMatcher->getCurrentRouteMatch();

  if ($currentRouteMatch->getRouteName() === 'entity.user.canonical') {

    /** @var \Drupal\Core\Session\AccountProxyInterface */
    $currentUser = \Drupal::currentUser();

    if ($currentUser->isAuthenticated() && $currentUser->id() === $currentRouteMatch->getParameter('user')->id()) {

      foreach ($variables['items'] as $name => $item) {

        MODULE_set_user_profile_link_as_active($variables['items'][$name]);

      }

    }

  }

}

/**
 * Sets a menu item's link as active if it's to the user page.
 *
 * @param array $item
 *   An array of menu items.
 */
function MODULE_set_user_profile_link_as_active(array &$item) {

  if (isset($item['url']) && $item['url']->getRouteName() === 'user.page') {

    $item['in_active_trail'] = TRUE;

  }

  if (!empty($item['below'])) {

    foreach ($item['below'] as $name => $below_item) {

      MODULE_set_user_profile_link_as_active($item['below'][$name]);

    }

  }

}