Restrict product tags archive to certain users

You could setup a redirect at the top of the archive page template for users that don’t match your criteria, something like:

$user = wp_get_current_user();
$allowed = array( 'editor', 'administrator' );
$redirect_url="https://url-to-redirect-to";
if ( ! $user || ! array_intersect( $allowed, $user->roles ) ) {
   wp_safe_redirect( $redirect_url, 401 );
   exit;
}

The check for $allowed and $user role/meta depends on what you want to check for.