One of the things I've noticed is that Signal doesn't seem to care about privacy at all. They care a lot about security though, which is a different thing, and tell you that's privacy.
Pros
Free
Very good encryption
Almost no metadata kept
Protocol independently audited
Seamless to use on Android
Disappearing messages
E2EE text, voice, and video group chat
Requires a valid phone number to register
Hosted on Amazon Web Services (AWS)
Edit to clarify: Signal sets up a background connection instead, which still results in real-time notifications (the same way that Wire works on a phone without Google Play services)
A year ago or two, I wanted to build Signal for Android without the proprietary library that talks with google play services. It was possible by modifying the source code a bit, because the code checks for the presence of the handles the absence of the Google play Services and enables some sort of fallback.
I would not know if it is still the case today, I don't currently own an Android device.
You can manage to use Signal with most features without the need to run proprietary blobs by registering your phone number using signal-cli or axolotl (and maybe alternatives, but I haven't tried). They can run on a regular desktop or on a GNU/Linux phone, and then pairing Signal-Desktop with it. This is not straightforward, and forget convenience on the phone for now (I haven't managed to make groups work on UIs based on signal-cli though they theoretically should, Axolotl does not fully support new groups and by that I mean it's missing essential features like accepting an invitation).
Then, the blobs you are running are "only" in your phone's modem, unless you also managed to use some service providing SMS from the internet.
This is totally unsupported because it depends on alternative Signal clients that are not allowed on the Signal's network. For some reason Signal-cli and Axolotl don't seem to have been asked to stop from the Signal team, but it happened to a Signal fork, Free-Signal, which only goal was to de-blob Signal. And they are in their own right to do so, I'm not questioning this.
This is painful, really. Signal is so close to be great. Matrix / Element works well enough. It has rough edges but I (re)-discovered that Signal has some too and I'm not speaking about this whole situation.