Fingerprints and facial recognition are not secure methods for unlocking your device. They are like passwords that you can never change. It's not just data leaks or malware that could cause this sensitive information to be lost. Even pictures you publish yourself that show your fingers or your face could put you at a disadvantage.
In some countries, the police are also allowed to use your fingerprints to unlock your device. There have already been court rulings on this in Germany and the USA.
If you have an iPhone, you can temporarily lock Face ID and your fingerprint by pressing a special key combination. For Android, lockdown mode is available on some devices, allowing you to quickly disable biometric features in an emergency. You can find out more about this in the links below.