Modify/change the default allowed tags for bbPress.

gistfile1.php

<?php
/**
 * Modify/change the default allowed tags for bbPress.
 *
 * The default list (below) is in bbpress/includes/common/formatting.php, L24-66.
 * Adjust below as needed. This should go in your theme's functions.php file (or equivilant).
 */
function ja_filter_bbpress_allowed_tags() {
	return array(

		// Links
		'a' => array(
			'href'     => array(),
			'title'    => array(),
			'rel'      => array(),
			'target'      => array(),
			'style'      => array(),
		),

		// Quotes
		'blockquote'   => array(
			'cite'     => array(),
			'style'      => array(),
		),

		// Code
		'code'         => array(
			'style'      => array(),
		),
		'pre'          => array(),

		// Formatting
		'em'           => array(
			'style'      => array(),
		),
		'strong'       => array(
			'style'      => array(),
		),
		'del'          => array(
			'style'      => array(),
			'datetime' => true,
		),
		'br'           => array(
			'style'      => array(),
		),
		'i'           => array(
			'style'      => array(),
		),
		
		// Document
		'div'           => array(
			'style' => array(),
		),
		'span'           => array(
			'style' => array(),
		),
		'p'           => array(
			'style' => array(),
		),
		'h1'           => array(
			'style' => array(),
		),
		'h2'           => array(
			'style' => array(),
		),
		'h3'           => array(
			'style' => array(),
		),
		'h4'           => array(
			'style' => array(),
		),
		'h5'           => array(
			'style' => array(),
		),
		
		// Table
		'table' 	   => array(
			'style' => array(),
		),
		'thead'		   => array(
			'style' => array(),
		),
		'tbody'		   => array(
			'style' => array(),
		),
		'tfooter'	   => array(
			'style' => array(),
		),
		'th' 		   => array(
			'style' => array(),
			'colspan' => array(),
			'align' => array(),
		),
		'td' 		   => array(
			'style' => array(),
			'rowspan' => array(),
			'colspan' => array(),
			'align' => array(),
		),
		'tr' 		   => array(
			'style' => array(),
		),
		
		// Lists
		'ul'           => array(
			'style' => array(),
		),
		'ol'           => array(
			'start'    => true,
			'style' => array(),
		),
		'li'           => array(
			'style' => array(),
		),

		// Images
		'img'          => array(
			'src'      => true,
			'border'   => true,
			'alt'      => true,
			'style'    => true,
			'height'   => true,
			'width'    => true,
		)
	);
}
add_filter( 'bbp_kses_allowed_tags', 'ja_filter_bbpress_allowed_tags' );