I wouldn't say most, but a large portion. You should be able to look up in advance which ones are funny about custom roms, the key words are safetynet or play integrety api.
My solution to this is put the bank apps that are annoying about it on an old phone (I knew I'd find a use for one eventually!)
YMMV. I'm on mobile but I think someone maintains a wiki page of compatibility.
Remarkably, Nationwide (UK) runs perfectly even without Google services. (Except it doesn't poll for payment confirmations but that's understandable. They're always fetched when you open the app though. Or it could be my setup). It's actually quite shocking and it speaks to Nationwide as being a decent organisation.
It's also not necessarily a downside. Having your banking app on your phone can be a risk of you often take your phone out in public
The absolute blocker is Google Pay. That isn't supported
> We are launching Curve Pay in beta for Android soon and plan to release it on iOS thereafter. This will allow customers to use Curve as their default wallet, just like Apple Pay or Google Pay.
…and with various German news sites reporting that Curve Pay is now available in Germany (and likely other parts of the EEA).
I'm in Switzerland, and both Neon (Hypothekarbank Lenzburg) and Zak (Banque CLER) work perfectly fine.
Google Wallet does not work, therefore I cannot use my phone to pay wirelessly with my Neon card, which is a shame.
The only apps I had trouble with were Twint (had to install it with F-Droid, as Play kept telling me it was not compatible with my device), and... the McDonald's app (which forces me to move my fat ass to one of their kiosks to order my food instead of doing it from the table).
As a GrapheneOS user I can speak of my experience: the app for my bank was working fine until 2 months ago, when after an upgrade it stopped working because of Integration API.
I will contact them to try to get them to support GrapheneOS, but I will not be holding my breath. I uninstalled it in the meantime and use my computer. If they ever require the app I would likely switch to a different bank.