OK, I experimented. I blocked all Local Storage and then successfully logged into my Bank of America, Key Bank, PayPal, and Discover Card accounts.

Jon

macOS 11.7.10, iMac Retina 5K 27-inch, late 2014, 3.5 GHz Intel Core i5, 1 TB fusion drive, 16 GB RAM, Epson SureColor P600, Photoshop CC, Lightroom CC, MS Office 365