Generally, they sell information in the order of risks. Apply for loans and credit cards- highest chance. Large volume CD and deposits - lowest chance (they want to keep this business in house)
Loans highest chance of your information getting cross sold. Especially if the bank doesn’t have cross products. E.g. if a bank offers home loans, but but not credit cards. If you get approved they might offer you a credit card as well, but from a different bank.
The terms are usually laid out in the privacy policy and T &C, most will allow you to opt out.
However, it may not always be a bad thing, if you have good credit scores and low debt, banks compete for your business. If you get a banking product like a car loan from another bank, your own bank might compete for that same product with better rates.
Back in the day, when I was in retail operations, I did all of this manually. If I saw a lot of checks from a customer’s account going to pay credit cards and bank loans at other banks, I would contact the customer and offer a competitive rate. Of course today you can mine all that information.
Bank never share such details to outsiders but it's data processing department when disposed off their documents non properly basis so details are shared unintentionally. the company taking data are supposed to use its own purpose of business. so beware of fraudulent calls msg asking for OTP, Access of Mobile, KYC, ATM Pin Changed, Block Account. Bank Never do such calls directly to customer. it send Notice and Officials Mails or Information on Mobile Banking App or Internet Banking Notification