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