Now that Signal no longer supports SMS messages, there is no reason to not use Molly-FOSS as your Signal client app.
Molly is a fork of the Signal app, providing an encrypted message database, in addition to other security related features.
https://molly.im/
Removing SMS support from Signal Android (soon)
https://www.signal.org/blog/sms-removal-android/
Still need to resolve an issue with Molly-FOSS having problems connecting to the network on my LineageOS device without any Google Play Services.
The original Signal app, however, does not have a problem at all registering my phone number on the very same device. Even though it initially does give a warning, I only needed to disable aggressive battery management to get instant notifications of new messages.
Now wouldn't support of #UnifiedPush be a great addition to Signal?
Anyway, so maybe the connection issue of Molly-FOSS is not related to the absence of the Google Play Services after all.
Adrian Offerman