Threema is not open source yet so I wouldn't use it for that reason. I did like their security whitepaper, though, and they do have some impressive clients (Mercedes-Benz, etc.).
Open source is a precondition. They can promise you the world, but if you can't build it yourself and get reproducible builds, who knows what's in there.
It seems that Threema charges for the app instead of requiring a phone number. Do they offer anonymous payment options like cryptocurrency or cash by mail?
I'm not sure how data protection works with Google Play and App Store payments, but I feel like this could be a potential privacy problem.