Always carry extra cash everyday to pay at stores, never have debit/credit card in wallet unless it's to withdraw more cash, never give stores your number or name to buy or reurn something, do not give legitimate info to register for a free store card, never register for a tap pay service on cellphone, buy a pre-paid credit card if you can buy it anonymously with cash, for Americans, use privacy.com for card masking.
If you exclusively use physical cash with change at stores and never give a name, there's no behaviour prediction to get from you or how to advertise to you. Online purchases are not as good for data mining and tracking because there's no geo location like paying with a card at a store that can be used to track your movements and at what time you were there.
I'm not zealous about it... I'm selling my privacy for 1.5% cashback to banks and for 5% to Amazon!
However, I'm consolidating my banking to fewer banks than earlier. And I stopped using services that aggregate financial accounts to provide insights - budgeting, projections, investment advice, etc.
On the other hand I use Privacy.com for smaller vendors, but more often for security reasons than privacy.
Monero for some services, like VPN.
Also, no real name or address in store loyalty programs.
Additionally to what people have said, I have set up several banking accounts with different banks. That way, no bank has the full picture of what I earn or how much I spend.
My problem is cash is really the only way to be truly private with your finances. Nothing else besides going great lengths using Crypto or gift cards is really private as far as I understand.
I personally hate using cash, it is just such a hassle to use when compared to a debit/credit card.
I always worry I don't have enough or I have too big of denominations, or I will fail at math and look like an idiot. It is annoying to carry around, if you live in a bad neighborhood it could be potentially dangerous to carry around.
I really wish there was a private mainstream finance option but I have yet to come across any.
Probably worth moving your e-commerce sites off your google, outlook etc. Proton mail would be good. I don't use open banking. Everything is debit card.
It's here in the UK, not sure about elsewhere, but a sort of standard for exposing financial data to 3rd party providers of apps etc. I don't know too much about it, but linking my banking to other services didn't sit well with me.