Carrying ID or not carrying ID should not be a problem. Being stopped by Police or an immigration officer where there are no reasons to suspect you are here illegally or have commited a crime is wrong. They need to explain why you have been stopped.
Its entirely up to you if you produce ID and they have no rights to search you unless they have suspicion you are carrying something illegal.
The rule book all makes sense to me. Perhaps some on here would have preferred it if the Nazis were in power then we would all have to show id and maybe wear a star on our clothing.