Adding the is_front variable to a Paragraphs template
You should be able to add this with a preprocess function in mytheme.theme of your theme.

/**
 * Implements hook_preprocess_paragraph().
 * @param $variables
 */
function mytheme_preprocess_paragraph(&amp;$variables) {
  $variables['is_front'] = Drupal::service('path.matcher')-&gt;isFrontPage();

  // Ensure the cache varies correctly.
  // Drupal 8.2.x or lower
  $variables['#cache']['contexts'][] = 'url.path';

  // Ensure the cache varies correctly.
  // Drupal 8.3.x+
  $variables['#cache']['contexts'][] = 'url.path.is_front'; 
}


This should add is_front as a variable to any paragraph twig template. Clear cache after adding this code.

Per 4k4's comment, if this is Drupal 8.3 you will also need to add a cache context.