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.
It shouldn't matter as long as we understand the difference. In any case, people won't be in a position to reject CBDCs or do anything about it. The governments will straight up just make everything online and force you to use those wallets. What everyone can do though is to lay more stress in personally being invested into bitcoin, as well as actual commodities, to whatever extend feasible.
CBDC may also be an opportunity for Bitcoin to help increase scalability and liquidity, it will make Bitcoin more priceless.
This is an otherwise thought in contrast to your topics title.
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The OP is just talking about the fact that bitcoin has already caught the fiat overlords unaware. With institutional interest by some of the biggest private corporations, it is clear that even they don't like paying negative interest rates. For the corporates, bitcoin may be the only bargaining chip against monetary mismanagement. For the people, when the government transitions whole countries to CBDCs, bitcoin will naturally become the currency of the free internet.