Classy/Bartik node teaser with taxonomy term reference value displayed as H2 on front page

If you assign a taxonomy term reference to a teaser the taxonomy term (value) is displayed as a whopping H2 (with a tiny label).

Example: I have a taxonomy 'module_status' and a term 'NO_D8', used in a taxonomy term reference field in a custom type 'module'.

Result (with Twig debugging on) in front page:

<div class="field__items">
              <div class="field__item">

<!-- THEME DEBUG -->
<!-- THEME HOOK: 'taxonomy_term' -->
<!-- FILE NAME SUGGESTIONS:
   * taxonomy-term--10.html.twig
   * taxonomy-term--module-status.html.twig
   x taxonomy-term.html.twig
-->
<!-- BEGIN OUTPUT from 'core/themes/classy/templates/content/taxonomy-term.html.twig' -->
<div data-quickedit-entity-id="taxonomy_term/10" class="contextual-region taxonomy-term vocabulary-module-status" about="/taxonomy/term/10" id="taxonomy-term-10" data-quickedit-entity-instance-id="0">
  
      <h2><a href="/taxonomy/term/10">

<!-- THEME DEBUG -->
<!-- THEME HOOK: 'field' -->
<!-- FILE NAME SUGGESTIONS:
   * field--taxonomy-term--name--module-status.html.twig
   * field--taxonomy-term--name.html.twig
   * field--taxonomy-term--module-status.html.twig
   * field--name.html.twig
   * field--string.html.twig
   x field.html.twig
-->
<!-- BEGIN OUTPUT from 'core/themes/classy/templates/field/field.html.twig' -->

            <div data-quickedit-field-id="taxonomy_term/10/name/en/default" class="field field--name-name field--type-string field--label-hidden field__item">NO_D8_YET</div>
      
<!-- END OUTPUT from 'core/themes/classy/templates/field/field.html.twig' -->

Looks roughly like this:

NO_D8_YET