.white { background-color: transparent ! important; }
.red { background-color: red; }
div.t1 p { background-color: lime; }

 <div class="t1">
  <p class="red">This paragraph should have a green background</p>
  <table>
   <tbody>
    <tr>
     <td>
      <p class="red">This paragraph should have a green background</p>
     </td>
    </tr>
   </tbody>
  </table>
 </div>
 <table>
  <tbody>
   <tr>
    <td>
     <p class="white">This paragraph should be unstyled.</p>
    </td>
   </tr>
  </tbody>
 </table>