You can't use it without installing closed-source Google Apps (Play Services for GCM at minimum), and means you agree to hand over your phone metadata to Google (per the OP's top-thread). Moxie has stated he is open to consider high quality PR's to add Websocket functionality. (Removing close-source binary blobs would be a prerequisite to distributing on anything other than Google Play to though, which Moxie's also said isn't on the roadmap - I assume primarily because of resources).
In the meantime, Conversations.IM has OMEMO and Vector.IM has Olm/MegOlm.
There's not a lot of good voice options. Vector.IM's just added WebRTC, which is meant to be DTLS secured. CSipSimple does ZRTP, but it hasn't been updated in a long time.
None of the apps mentioned above has been audited and scrutinised to the extent Signal has.
If you really need privacy & security, CopperheadOS is the only Android distro AFAIAA that fits the bill at the moment.