SimpleX has very good encryption and does not require any identifiers. I have not seen any credible critique of their white paper.
Session does not require any identifiers and some have debated if the encryption technology is good enough to thwart advanced attacks, with the developers responding that it is. I am not sure whether the criticism is valid.
Briar is the only messaging App that allows Bluetooth mesh network communication which could be useful in a scenario in which society unexpectedly breaks down or normal networks can't be used.
(Threema is considered excellent and is also an App that requires payment, with any concerns about that could bring up. Threema may be a good option for corporations or groups requiring encryption, especially since there may be more support if there are issues since it's a paid service. If there are protocol concerns, I don't know about them and it may be worth looking into.)