First of all, there is no need for fear. Cryptocurrencies are in an early stage, but the technology supporting them is very strong. The right mentality is precaution. Be serious about the way you manage your money, because there is no central bank to refund it if you lose access to it.
Now, in iOS you can’t check that the app is running the same code than in GitHub, but that’s a problem with Apple, not the developers. Most of the time, you could assume that it will be the same code. Many people use those application and there haven’t been lots of problems with that.
However, Apple has put strong handcuffs in the hands of their users to prevent them from controlling their software and their devices, so there is nothing preventing them from tampering the code of the application. Android is only a little bit better, because you can manually compile the APK from source but Google is trying to make Android a proprietary system.
To avoid losing your funds, you should stick to the best security practices:
- Keeping backups of all your seeds (also physical, if possible).
- Always using reputable software (only free/libre) to manage your coins.
- Never leaving your funds in exchanges for too long (not your keys, not your nanos).
- Using paper wallets or (even better) hardware wallets to store securely offline.
This way you will improve your security a lot and the risk of loss or theft will decrease to a minimum.