Signal messenger uses reproducible builds. You can compare the source code to the app that's published to the app store to confirm that they're being honest.
I don't know if any other competitors who do the same. As Signal messages are end-to-end encrypted, Even if their servers were compromised, your messages would still be secure. As they use a rotating key, unlike manually using PGP, even if one of the keys was intercepted, they would not be able to decrypt any of your other messages. Using PGP, if someone steals your private key, all your messages are now vulnerable.
https://signal.org/blog/reproducible-android/