The problem is that your ordinary citizens do not know the difference between the two. If CBDC is "government supported," then it must be legal, right? Educating the public in some way about actual value support seems to be the only way to ensure that CBDC has nowhere to go.
Also, if you interact with CBDC in any way, the CBDC issuer can actually develop a full financial online profile of yours. They might be developing very sophisticated interfaces for CBDCs and cryptocurrencies such that they ultimately get to know exactly who you are and what you are up to. The herds will fall for it I guess.