Of course the EU and member states must work to ensure that people moving from one country to another understand their obligations and their rights in areas like health, road safety and further education.
The E.U. is more than just a trade organization or a common market; it is a guarantee of democracy, freedom, justice, and human rights. Nations cannot stay in the E.U. if they do not respect these guarantees.
It is not viable for one country to demand a right to increase and upgrade its nuclear weapons capabilities while asking others to eliminate theirs.