Signal has a Google Play Services dependency for notifications, so it won't work properly without installing the whole Google package.
Open Whisper Systems (the developers of Signal) apparently don't want to replace it or even just build in a fallback [0], and even fought with the LibreSignal developers, which is a fork that removes this dependency, and told them to stop using their servers [1], which lead to LibreSignal being discontinued.
I don't know what the heck is going on with this, but yeah, it's not pretty.
I am using it and while it's not really working for me (I suppose an update broke it), it's enough to convince Signal to install.
It doesn't receive push notifications but I still receive messages once I run the app in the foreground (a thing I almost consider a feature now and not a bug)
from 2:
> I understand that federation and defined protocols that third parties can develop clients for are great and important ideas, but unfortunately they no longer have a place in the modern world.
¹ https://github.com/microg/android_packages_apps_GmsCore/wiki
² https://github.com/LibreSignal/LibreSignal/issues/37#issueco...