There are a couple ways to achieve this but they will require editing all your themes. This method removes the tables with only two edits and can be un-do easily.

Files to edit:
includes/page_header.php
includes/page_tail.php

Steps :
Open includes/page_header.php and delete or comment OpenTable(); . There is only one so it will be easy to find it.

Next, open includes/page_tail.php and delete or comment CloseTable(); . There is also one so finding it is not difficult.

That's it! Save and upload and now no more tables around your forums :)