Yes, XMPP, a long-standing protocol that’s also not a walled garden, doesn’t require a phone number or even a phone. For android I use the Conversations client combined with Dino on computers. Currently logged in to a handful of devices synchronously. You can choose what server to make an account on; conversations.im I found to be reliable. Drawback is Signal doesn’t let you bridge to it from anywhere outside of Signal. So I have accounts on both.
counter-question: Is it impossible to be private offline?