Zeekunst Berichtenbox and Triodos bankieren both work fine without Google Play Services. Even the Albert Heijn, Afvalwijzer and NS apps do (without notifications).

Yes it works (with or without GPS)

I have tested:

Hema
NS
Zalando
Bol
Albert Heijn
To Good To Go
ANWB
Odido (also Without GPS)
Rabobank (also without GPS)

I can confirm the Triodos banking app is working well, there is no Play Store installed, my aquintance used Aurora Store in order to download the app instead.

I use the ABN AMRO website with the identifyer hardware myself, which is working fine, I have not and will not install the app.
I have no Play Store installed myself.

Really, the only problematic thing I'm experiencing is contactless (NFC) payment. Like many others, my bank has removed contactless payment functionality from their app and is referring to Google Pay. Google Pay doesn't work on GrapheneOS because Google doesn't acknowledge it as a valid OS (yet).

2 months later

I didn't read anything about the KNAB-banking app. Unfortunately I can not find anything on the web. Customerservice knew nothing about Graphene. Does anyone know?

    Satoichi I can install the app (with google play services) and it runs normally, but I haven't registered, since I have no KNAB account.

      Michiel Thanks Michiel! I ran KNAB before on a phone with Lineage OS with Gapps installed. It worked , but i wasn't able to scan QR codes needed for Ideal payments...
      (I'm about to buy a Pixel 9, but exploring what works and what doesn't).

      11 days later

      I installed Graphene on a new Pixel 9 with Android 15 and KNAB works perfectly. Furthermore I was very surprised that Revolut is running without any problems, though I read on several sites that it wouldn't run, because of the absence of a verified OS...
      Happy here!