How to add Taxonomy Vocabulary Machine Name in Body Class in Drupal 8

Use HOOK_preprocess_html() function and copy the following example to your code:

function HOOK_preprocess_html(&$variables) {

  if (\Drupal::routeMatch()->getRouteName() == 'entity.taxonomy_term.canonical') {
    // load the term entity and get the data from there
    $term = \Drupal::routeMatch()->getParameter('taxonomy_term');
    $variables['term_id'] = $term->id();
    $variables['vocabulary_id'] = $term->bundle();
    
    $variables['attributes']['class'][] = 'taxonomy_' .  $variables['vocabulary_id'];
  }

}

Do not forget to clear the cache if you do not have hook already registered.

You new class should be like taxonomy_MACHINE_NAME and you can widely use it in your CSS now.