Proper way to replace the_content only for pages created by custom plugin

You need to return the filtered content, try like this:

add_filter('the_content', 'emd_content');  

function emd_content( $content ) {
  if ( is_page('Member Directory') ) {
      include dirname( __FILE__ ) . '/content-members.php'; 
    }
    elseif ( is_page('Contact Members') ) {
      include dirname( __FILE__ ) . '/content-member-contact-form.php'; 
    }
    else {
        return $content;
    }
}

But the better way is to use custom page template for those pages.