All banks and bank-like institutions you might have access to will comply with the same anti money-laundering and know-your-customer regulations. It’s not really up to the individual bank to decide.

The “Swiss bank account” is largely a thing of the past, as they are forced into data-sharing agreements with the United States and possibly others. And even so, you need to be a Swiss national to qualify for a bank account there.

You can use cash as much as possible when it’s an option, of course. It’s less convenient, but privacy often is.

Monero

EU has regulatory requirements that banks need to satisfy if they want to operate there. Look into KYC requirements and what data they need to store about money transfers if you want to know what data banks absolutely have to collect.

Cash, monero, prepaid visa cards.

Assuming you’re in north america, there is no privacy respecting traditional bank. Use cash or monero if you want to hide your transactions

Noob question: do you think that banks sell info regarding your/our transactions to third party?