Every bank I've used has had a pretty absurd amount of trackers that I've blocked, often 5-10+ third party javascript domains. I don't know of any that don't have any, but I'm sure some small ones exist somewhere.
There doesn't appear to be a huge market for services that do little/no tracking, as users are all unaware of the tracking that services do to begin with, so they would not even notice the difference.
As a US citizen I don't see much that can be done. Although I don't trust the third-party scripts, the bank obviously does, given they're all large analytics platforms.
Banks rely on a very small number of software vendors, so that the apparent abunance of bank options is all but eliminated at the middleware tier.
"What Is Your Bank’s Security Banking On?"
FIS, Fiserv or Jack Henry ... collectively control approximately 70 percent of the market for bank core processors (according to FedFIS.com, Fiserv is by far the largest).
There doesn't appear to be a huge market for services that do little/no tracking, as users are all unaware of the tracking that services do to begin with, so they would not even notice the difference.