First, you're conflating privacy with anonymity.
Secondly, they are one of the few orgs (maybe only?) that have been subpoenaed multiple times and they've published documented evidence [0]
that even when compelled by law to present all the info they have on any specific user, all they know is:
- The date you created an account
- The last day (not time) one of your clients messaged their
Feel free to trust whoever you want, but the source code to Signal's clients and server are open for anyone to criticize, and they have been. They're not perfect, nobody is, but they're also one of the few orgs out there showing that they're willing to put up or shut up.
Criticize in a constructive manner. Don't be dismissive and spread FUD by stating "I don't trust them" without backing up understanding the Signal threat model and mixing up privacy & anonymity.
That's the option I give people and have converted many. I have Signal, it has more modern features than SMS, is basically Whatsapp, but run by a non-profit org. If you don't care to install it, use SMS.