New laws always overrule older laws. Most legal systems, including the EU, have a constitution, that is harder to change and that governs what laws are allowed or not (the UK is rather unique in not really having such a law, so that in principle Parliament is free to pass any law they want).

Enshrining a right to private communication and online anonimity into the EU constitution would probably prevent such laws from having any hope to go into effect, but that's a massive undertaking that I don't think would easily succeed.