Android: textInput: secureTextEntry toggle causes keyboard change; keyboard does not automatically come up

Description:
When enabling the user to toggle the secure text entry flag on a text input, on Android, two issues are occurring:

1. The keyboard does not automatically come up when rendering; the user must tap on the field.
2. Tapping the 'eye' icon to toggle the secureTextEntry flag from false to true switches the keyboard type.

React Native version:

System:    OS: Windows 10 10.0.17134
    CPU: (4) ia32 Intel(R) Pentium(R) CPU G4560T @ 2.90GHz
    Memory: 1.65 GB / 7.43 GB
  Binaries:
    Node: 12.10.0 - C:\Program Files (x86)\nodejs\node.EXE
    Yarn: 1.10.1 - C:\Users\mjfiandaca\AppData\Roaming\npm\yarn.CMD
    npm: 6.13.4 - C:\Program Files (x86)\nodejs\npm.CMD
  SDKs:
    Android SDK:
      API Levels: 23, 25, 26, 27, 28
      Build Tools: 23.0.1, 25.0.1, 26.0.3, 27.0.3, 28.0.0, 28.0.3
      System Images: android-23 | Intel x86 Atom, android-23 | Google APIs Intel x86 Atom, android-23 | Google APIs Intel x86 Atom_64, android-26 | Google APIs Intel x86 Atom, android-26 | Google APIs Intel x86 Atom_64, android-27 | Google APIs Intel x86 Atom, android-27 | Google Play Intel x86 Atom, android-28 | Intel x86 Atom, android-28 | Intel x86 Atom_64, android-28 | Google APIs Intel x86 Atom, android-28 | Google APIs Intel x86 Atom_64, android-28 | Google Play Intel x86 Atom
  IDEs:
    Android Studio: Version  3.5.0.0 AI-191.8026.42.35.6010548
  npmPackages:
    react: 16.8.6 => 16.8.6
    react-native: 0.60.6 => 0.60.6

Steps To Reproduce

1. Sign onto the provided snack.
2. Intermittently, the keyboard will not come up (I tested this several times; sometimes, no keyboard, sometimes, app starts, flashes, and then the keyboard comes up).
3. Tap on the 'eye' icon to toggle the secure text entry.
4. Notice the keyboard changes.

Expected Results

The keyboard should not change based on the secure text entry value.

Snack, code example, screenshot, or link to a repository:

https://snack.expo.io/@mjfiandaca/toggle-securetextentry

Comienza con la reproducción enlazada en Snack y el comportamiento de Android TextInput descrito en el issue. Comprueba por separado el renderizado inicial y el cambio de secureTextEntry, y luego verifica que el teclado aparezca automáticamente y no cambie de tipo cuando se use el control del ojo.