I see people mentioning you can do card making with banks, which is true, but those banks already know your identity, and probably do worse with your data. The whole point of the intermediary is to mask your purchases from your bank.

Unless you're faced with Persona yourself and are trying to avoid it specifically, I'm not sure if it alone is a reason to avoid Privacy. Any online bank like this will require your identity. (Maybe you can contact them and ask for an alternative method.)