I'm able to use my banking app and apps for all of my credit cards of both LineageOS & GrapheneOS without Google Apps installed.
The one app that refuses to work for me?
DoorDash.
What the shit.
Discussion
On GrapheneOS, did you install them via GA, then remove it?
Installed via Aurora Store. I see lots of people having issues. I guess I'm lucky, my credit unions app works fine, CapitalOne, CreditOne & Avant credit card apps work, as do a few others I used previously on old cards. Some pop up an error but pressing the back button closes it.
I've sent my Pixel 8 in for a screen replacement and am currently running LineageOS (without root) on a Moto G5 5G until it is returned. No issues here either.
A few other credit unions and local banks in my area work fine without GApps as well.