You can't do any kind of banking without extensive privacy invasion these days. It's called KYC: https://en.wikipedia.org/wiki/Know_your_customer

Even if you found a bank with an open-source wallet application (you won't), they would still ask you your ID, your income, what you spend on, your mortgage, the list of countries you have accounts in, how much on each account, the size and color of your underwear, you're wife's shoe size etc etc.

Unless you find an employer that pays you in cash (you won't), you can't do anything private with your money anymore. Welcome to the 21st century dystopia.