Are we talking about the same EU? The EU does this for censoring and monitoring, not against it - and they're totally open about it too. Google "Zensursula"...
I would expect quite a lot of resistance to monitoring efforts, even if they are paid opt-ins (which will mostly be used by schools and employers, the same way they already use similar services that do the same).
Censoring of illegal content is much less controversial, and already happening to various degrees at the ISP provided DNS servers. You can make good arguments for transparency and oversight by the courts, but that's as far as it usually goes. Hard to argue that illegal things should be publicly accessible.
It's not at all hard to argue that illegal things should be publicly accessible. I find it impossible to argue that governments should be able to decide what information is publicly accessible. There is no relationship between legality and morality.
From the perspective of public accountability, this is a step forward compared to the current status quo - where some countries implement blacklists and some don't, some are accountable and some aren't, etc etc. The EU dns would then work as public registry of such activities, also clarifying and harmonising the bar for acceptable censorship (i.e. opposition activity in Hungary? Not bannable...).
Censoring of illegal content is much less controversial, and already happening to various degrees at the ISP provided DNS servers. You can make good arguments for transparency and oversight by the courts, but that's as far as it usually goes. Hard to argue that illegal things should be publicly accessible.