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.
Most people are not used to think on their own, they are sheep and they believe whatever they are told and this means that the majority are going to still look at bitcoin with suspicious eyes and are going to prefer whatever has the stamp of approval of the governments, the only way this is going to change rapidly and massively is if there is an economic crisis so acute that people do not have any option left but to challenge their own beliefs, and even if we know it is coming no one really knows when it is going to happen.