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.
Indeed, the stablecoins of the central banks of states will provide an opportunity to appreciate the benefits of a decentralized cryptocurrency. People will compare the capabilities and convenience of each payment system and choose which one to use. However, this will be a long process and will take a long time. States and their governments can also try to lessen the impact of cryptocurrency through tighter regulation. However, the cryptocurrency needs to go through this, from this it can only become stronger.