From RN docs:
For iOS 11+ you can set textContentType to username or password to enable autofill of login details from the device keychain.
This means that setting textContentType to something different than username or password should disable autofill on iOS keyboard. But I noticed that setting secureTextEntry prop to true in the TextInput component also enables autofill even if textContentType is not username or password. This is true except for one particular case, when textContentType is set to "oneTimeCode". This disables autofill even if secureTextEntry is true.
When I want to hide the password autofill and still set secureTextEntry to true, I just do this:
<TextInput
secureTextEntry
textContentType="oneTimeCode"
/>
There are other situations where textContentType is not "username" or "password" and secureTextEntry is false but autofill is still shown. Setting textContentType to "oneTimeCode" also works here.
<TextInput
textContentType="oneTimeCode"
/>
This is more like a hack than a solution, but it works for me.