Facebook plugin shows existing comments

I don’t use this plugin, but it looks like this comment template is loaded with

add_filter( 'comments_template', array( 'Facebook_Comments', 'comments_template' ) );

The simplified structure of this comment template looks like:

if ( have_comments() ) :
    // ...
    wp_list_comments( $_comment_options );
    // ...
endif; 

$_facebook_comments = Facebook_Comments::comments_box();
if ( $_facebook_comments ) {
       do_action( 'facebook_comment_form_before' );
       echo '<div id="respond">';
       echo $_facebook_comments;
       echo '</div>';
       do_action( 'facebook_comment_form_after' );
}

Then you could try to let have_comments() return false to skip the WordPress comments part.

Checking the core, we find that:

function have_comments() {
    global $wp_query;
    return $wp_query->have_comments();
 }

where the class method is defined as

function have_comments() {
    if ( $this->current_comment + 1 < $this->comment_count ) {
        return true;
    } elseif ( $this->current_comment + 1 == $this->comment_count ) {
         $this->rewind_comments();
    }

    return false;
}

You can then try

function skip_wp_comments() {   
    global $wp_query;
    $wp_query->current_comment = 999; // large number
}
add_action( 'template_redirect', 'skip_wp_comments' );

to let have_comments() return false.

If that doesn’t work you could overwrite the comments_template filter to use your own template or try to play with the comment_count part.