While I'm sure a lot of people will obey the EU diktats like sheep, the reality is that there is a huge difference between announcing a regulation and actually having the means to enforce it.
The most I suspect they'll be able to do is block on-ramps to anonymous wallets and try to intimidate businesses taking crypto payments. They'll find it harder to stop peer-to-peer or in person transactions. They'll also find it hard to break the habits of the French and other cultures that like to keep a bit of "mattress money" for exactly this kind of situation.
I wonder how long before we see a "European Spring" when enough people have had enough ?