Workaround 3rd party captcha or authentication that does not load on the front end

/**
 * This snippet returns the authentication to its WP native
 * state if there is no $_POST['wp-submit'] (which is the 
 * native WP login submission button).
 *
 * Note: The priority (99 in the example) may have to be adjusted
 *       to a later priority (i.e. higher number) depending on
 *       when the third party plugin fires its custom authenticate
 *       filter function.  If the plugin fires at a higher priority
 *       number, you'll need to adjust this to a value higher than 
 *       that.  For example, if the plugin runs at priority 1000, 
 *       then your reapplication of WP's authentication needs to 
 *       run at 1001 or higher.
 */
if ( ! isset( $_POST['wp-submit'] ) ) {
    add_filter( 'authenticate', 'wp_authenticate_username_password', 99, 3 );
}