As sad as this may sound most people are financially illiterate, despite their finances being so important that they dedicate a great deal of their time to try to earn money, they do not want to stop and think about the moves they need to do to improve their financial situation, so even if CBDCs and cryptocurrencies are completely different most people will believe whatever they are told, something which will hinder the adoption and the development of cryptocurrencies in general.
You can bet that governments will do everything in their power to discredit the use of cryptocurrencies once CBDCs are launched for public use. After all, they don't want to lose control over the economy. A CBDC will give governments and central banks more power as everything will be widely accessible in a distributed ledger they control. We cannot say the same about paper money which is anonymous by design (sort of).
Some people will still use traditional cryptocurrencies because they don't want to give away their privacy. But the rest will use CBDCs to avoid getting left behind in the dust. I wouldn't worry about government-issued digital currencies as long as decentralization wins in the long run. Who knows if CBDCs live alongside crypto for generations? Just my thoughts