This will disable nonce checking for logging out – on your head be it:
add_action( 'login_form_logout', function () {
$user = wp_get_current_user();
wp_logout();
if ( ! empty( $_REQUEST['redirect_to'] ) ) {
$redirect_to = $requested_redirect_to = $_REQUEST['redirect_to'];
} else {
$redirect_to = 'wp-login.php?loggedout=true';
$requested_redirect_to = '';
}
/**
* Filters the log out redirect URL.
*
* @since 4.2.0
*
* @param string $redirect_to The redirect destination URL.
* @param string $requested_redirect_to The requested redirect destination URL passed as a parameter.
* @param WP_User $user The WP_User object for the user that's logging out.
*/
$redirect_to = apply_filters( 'logout_redirect', $redirect_to, $requested_redirect_to, $user );
wp_safe_redirect( $redirect_to );
exit;
});