.white { background-color: transparent ! important; }
.green { background-color: lime; }
div > p.test { background-color: red; }

 <div>
  <p class="white test">This paragraph should be unstyled.</p>
  <div>
   <p class="white test">This paragraph should be unstyled.</p>
  </div>
 </div>
 <table>
  <tbody>
   <tr>
    <td>
     <p class="green test">This paragraph should have a green background.</p>
    </td>
   </tr>
  </tbody>
 </table>