Ok, I’m a lineageos/microg user (not /e/) but I find this list useful so here’s some updated info:
Nordea Tunnuslukusovellus (Nordea ID) works for me without any extra steps (no need to enable device registration, google account or anything)
Valo dating app (see https://play.google.com/store/apps/details?id=fi.kotisatamanvalo.app&hl=en_US) requires device registration and Google Cloud messaging to be enabled, otherwise you can’t log in to the app. Account registration also seemed to “fail” with error message when those were not enabled but was successful, a confirmation was sent to the email. But login does require those steps.
I will post other issues later if I spot any.