A lot of apps rely on google play services. It mostly depends on how much of google play services an app requires as to whether it'll work on a degoogled phone or not.
CalyxOS includes microG, which solves the compatibility issue for some of Google Play Services' most essential features, including push notifications, better geolocation, and map rendering. microG also keeps Google's in-app ads disabled.
The gp mentioned government id apps specifically. Those along with banking apps are the ones I've heard having the most trouble without actual google play.
The problem with degoogled phones isn't not accessing the google play store, it's not having the confusingly named google play services.
https://en.m.wikipedia.org/wiki/Google_Play_Services
A lot of apps rely on google play services. It mostly depends on how much of google play services an app requires as to whether it'll work on a degoogled phone or not.