This rollercoaster is wearing me out. I hope this finally settles it!
The most obvious mechanism is a constitutional amendment, but in the U.S. the only amendment to be drafted and adopted in modern times is the 26th amendment (1971), 54 years ago. (The 27th amendment had a weird status where it was belatedly adopted with a 200-year delay.) It's hard to imagine many constitutional amendments actually being passed now because it's been challenging to find consensus on many things within U.S. politics lately.
I don't know that the EU at a supranational level has any mechanism at all to ban future EU directives. Maybe they could decide to remove something from the list of areas of competence of the EU? But Chat Control is under the "Area of Freedom, Security and Justice" and I can't imagine the EU deciding that that should be abandoned as an area of Union competence.
Edit: The international human rights treaties, at least in regulating law enforcement, have tended not to follow the idea that some kind of regulation or law enforcement power is completely off-limits, but just that they need procedural safeguards -- especially for surveillance and investigatory powers. In this case, Chat Control opponents (including me) would like it to be completely off-limits, but the human rights instruments arguments might more naturally go into "did they create enough surrounding rules and mechanisms about how it's used and how it's regulated?" rather than "can we just say governments just can't make this rule?".
It's the task of parliaments, governments, and courts to reevaluate and resolve all these contradictions over and over again. It's tedious and takes a lot of resources, but that's the price for democracy.
The constitution of the Democratic People's Republic of Korea (i.e. North Korea) famously guarantees freedom of expression as a fundamental right for the people. That hasn't stopped the government from trampling all over freedom of expression, though. The EU is of course nowhere near North Korea in terms of what is considered acceptable, but don't ever trust that the words in the constitution will be enough to keep the government from doing something.
Yet still that was never enough for a clear and definitive "no".
It is very likely that the people in favor of this would still try to push it through, or let that happen. They know that the legal battle afterwards to determine its unlawfulness would take years.
And during that time it could already be put it place. And once the legal battle is over (and likely won) severe damage is done and they could still adapt the law or just offer companies to continue doing this "voluntarily". And personally I wouldn't count on Apple, Google, or Facebook to roll this back quickly in that case once they've put it into place.
Speech is restricted the world over for things (fraud, threats, libel/slander, secrets, and more), and we're almost universally in favour of that.
It's a balancing act, and the point where we set the balance is difficult, and constantly changing (should we allow speech that encourages the persecution of other people, sometimes called "hate speech" or should people be allowed to advocate for the murder/rape/extermination of other human beings because of the way they look)
That's not to say that private communication can't already be illegal; mere 'conspiracy' is a crime in many places. Yet the level of surveillance that would be enabled by legislation like Chat Control is greater than any other in history. Even notorious agencies like the Stasi had to pick and choose their targets based on prior suspicion, simply because of the logistics involved in traditional surveillance.
We don't fully know what effects this kind of unceasing, universal monitoring would have on society, and what little historical precedent exists doesn't bode well. Restrictions on public speech however are pretty well understood; we've had censorship in various forms pretty much everywhere in the world at one point or another. We can look to history for lessons about what happens, and can properly discuss (even if not agree!) about when censorship is good or bad for society.
Edit: To anyone reading and thinking of joining in to any of the discussions, the message is clear - Facebook or Reddit level of inanity is all you will find here.
Sure, there is the rollercoaster, ups and downs, small wins and losses going on all the time. But look at the general trends - these freedoms that we enjoyed are by and large being chipped away, it's all trending down, worldwide. It's two steps back, one step forward. Maybe CC doesn't get put in place this particular time, but they will ram it through eventually, at some point the right angle will be found to make the right people vote for it. Then the battleground will move onto something even more egregious, and so on. I'm not seeing why there would be a sudden reversal of this trend in the coming decades.
In fact, if ChatControl does fail, they have already planned to include this in ProtectEU - a larger package coming soon...