https://www.privacyguides.org/en/real-time-communication/

I like Element.

It's a matrix client. Polished and nice. It's ok all the platforms under an Apache license. No phone number required. You've got federation on matrix as well, so just sign up on any server.

XMPP. It's an old standard, there are servers you can get an account with or you can host your own. And with OMEMO encryption everything is end to end encrypted.

Briar

Matrix is great, Element has a really nice UI for it. Signal also does work without a phone number, in fact it doesn't really work for SMS anymore. Signal provides P2P for any communications with another Signal user. Matrix supports P2P as long as you set it up (encrypt a channel) and I think DM's are P2P

Edit: So Matrix is cool, End to End, NOT P2P, and probably the right decision for OP.

Signal is great, Element (matrix) is great, but I personally think SimpleX did a fantastic job so far, and I really want them to succeed.

I guess Matrix would be your best option then. I use Schildichat as client, which is a fork of Element with some extras.

But if you can't get a plan, why not get a prepaid burner SIM? You can buy a prepaid card for minimal amount and you generally keep the number at least for a year, and you put in 5~10 euro each year you can keep it active endlessly.

A lot of things require a phone number. Here, the goverment needs you to have one, but also most workplaces and even the DHL. Getting a cheap trow-away sim isn't a bad option. Especially since pre-paid SIMs aren't connected to your name like those on a plan are.

Protonmail? Matrix?

Self host your own istance of Matrix

Table comparison of many messengers: https://www.messenger-matrix.de/messenger-matrix-en.html

I mostly use Signal but also Threema for a few contacts (you don't need a phone number for Threema, but it is not free - around 4-5 € one-time-payment).

You could try Session. It makes a session ID like this . This can be used to contact people or for people to contact you. I’ve used it to talk to my SO a bunch of times.

Simplex, element(or most matrix compatible messengers) session, bchat. If the goal is to get your family to switch over though good luck.

I do have something against signal! Phone number, removing SMS support, MobileCoin, lack of federation...

Sadly, my friends/family are sick of swapping and I've found element/session to be unreliable or overly complex, so I stick with Signal because it's still much better than SMS.

Session

I'd suggest SimpleX, personally! Not only does it not rely on phone numbers, but because you add people through single-use links instead of using identifiers, there is no contact information of yours to be shared without you actively choosing to share it with someone yourself. I'd say it's pretty approachable, and the actual messaging experience is packed with a nifty feature set.

Not free, but (finally) open source: Threema Libre

FSF India made a visual chart comparing messaging applications.

Does anyone have any recommendations for Element chat groups to join? All I find when I DuckDuckGo it is recommended clients that use Matrix, coding stuff, or weird sounding mathematical principles. Any groups involving FOSS discussions or ttrpgs would be great!

If you have to give up your phone number to register why would you get Signal over Telegram? All the people you aren't supposed to talk to are on Telegram and not Signal, so if you're giving up your phone number, why pick Signal? Because it's FOSS? What's the difference in outcome? Both end in a phone number request from the government that the service will comply with.