Banks have been around for hundreds of years. All I'm proposing is that there is a legal right for people to hold a bank account of some form, where they are able to put their money so they don't have all their life savings in cash under the bed. I'm not suggesting that we ban cash at all, just that people have a right to securely store their money and the option to use cashless transactions if they choose.
Being legally required to hold a bank account use cashless transactions is just as much of a violation of one's rights as being barred from opening a bank account and being forced to use cash for all transactions. Two sides of the same coin, so to speak. It's not about allowing people to transact in cash, but allowing them alternative choices, all of which should be legal.
If you can't hold a bank account (because the banks have decided you're not allowed one for whatever reason), you need to use cash for everything. This means you always have a relatively large amount of cash on you. Not only are you now at greater risk of burglary or robbery, the consequences of being a victim are now even greater. You also can't put money in a savings account, or pay for things online.
I've had my house burgled and had large amounts of cash stolen from me before. There was nothing the police could do. Even if they caught the burglar, the money wasn't coming back to me. It was a significant hit to my personal finances at the time.
Bank accounts and cashless transactions aren't just a way for the government to keep tabs on the population, they're also a form of security for the general population.