It seems that neochat is not working with E2EE encrypted chats. There is a message at the typing prompt which reads: "This room is encrypted. Build libQuotient with encryption enabled to send encrypted messages". It would be great of neochat adds support for that. Thank you!
libQuotient 0.7, which includes E2EE support is now in experimental. After it migrates to Sid I assume this package would start being built against libQuotient 0.7, thus prividing E2EE support.