Whatever you choose, the actual challenge will be convincing your family to use it just to speak to you.
F-Droid
F-Droid is an installable catalogue of FOSS (Free and Open Source Software) applications for the Android platform. The client makes it easy to browse, install, and keep track of updates on your device.
Matrix space | forum | IRC
Element (X) and Schildichat (Next)
On Android, there is Quicksy, and yes, it uses phone number sign-up for ease, but it seems more private than corporate apps.
Without phone numbers, there's Conversations.im. There are some public XMPP servers with open registration, but you would need to find one, e.g. sure.im by Tigase lets you make aan account, but I don't remember if calls work.
Are you looking to self-host something as well? Snikket is all-in-one chat+calls, but you would need to host a server. (Still based on Conversations and XMPP)
Jami, Trifa or Nextcloud Talk.