I don't use any banking apps, but from what I've seen on forums it can be hit or miss depending on the bank. I only use their webpages. If my bank required an app, I'd find a different bank.

Unfortunately it comes down to luck, you can check this crowd-sourced list to see if your banking app works. Users report whether or not they had (sandboxed) play services installed and what settings they toggled.

You won't be able to use GPay/Wallet at all due to lack of SafetyNet.