An TextInput must include secureTextEntry={true}, note that the docs of React state that you must not use multiline={true} at the same time, as that combination is not supported.
You can also set textContentType={'password'} to allow the field to retrieve credentials from the keychain stored on your mobile, an alternative way to enter credentials if you got biometric input on your mobile to quickly insert credentials. Such as FaceId on iPhone X or fingerprint touch input on other iPhone models and Android.
<TextInput value={this.state.password} textContentType={'password'} multiline={false} secureTextEntry={true} onChangeText={(text) => { this._savePassword(text); this.setState({ password: text }); }} style={styles.input} placeholder='Github password' />