add_filter( 'pre_comment_content', 'wp_specialchars' ); did the trick for me.

This removed the ability for users to post HTML (but not links for some strange reason) within comments:

add_filter( 'pre_comment_content', 'wp_specialchars' );

This removed the ability for users to post links within comments:

remove_filter('comment_text', 'make_clickable', 9);