After my MSFS 2020 upgraded to the latest version 1.39.12.0 (SU16), I was prompted to log into the Xbox/Microsoft account again.  For unknown reasons, the sign-in pop-up was unresponsive — preventing me from entering any information.
I tried various suggestions, including clearing Xbox Identities and resetting gaming services, etc, but nothing worked.

Although I still haven’t found the root cause and a proper solution, I did find a workaround that solved the issue for me:

1. Copy the email:  Copy the Microsoft account email address to the clipboard (Ctrl+C).
2. Launch the game:  Start MSFS 2020 and wait for the sign-in pop-up to appear.
3. Force the paste:  Repeatedly click the empty email field while continuously pressing Ctrl+V to paste the email address.
4. Be persistent:  It may take several attempts for the email address to successfully paste into the field.
5. Continue as normal:  Once the email is successfully entered, the password field should function normally.