The fairphone 3, with the /e/ android operating system, supports quite many apps also found in the Google Play store, although they do use their own repository (‘Apps’). In my experience / understanding all apps that don’t rely on libraries specific to Google could possibly work. What I mostly miss are banking apps and stuff that needs online payment.
I also miss the beeminder app, which I don’t find in their ‘Apps’ store. Is there a fundamental problem, or could this be relatively easily be provided?
Because /e/ is a terrible target for search engines, I’ll give the link here: /e/OS Fairphone 3 – eSolutions – deGoogled phones and services
And the FAQ: Which Android apps are compatible with /e/OS?
Most Android apps can be installed on /e/OS.
For now, we don’t support paid apps or in-app purchases.
As Google Mobile Services are not preinstalled on our phones, some apps that depend heavily on those services might not run properly. We update our system regularly to support more apps.
You can check if an app is already listed with our store here. In case an app isn’t yet listed in our store, you can request it directly from the store itself. We can also help you find other sources to access apps.