Sim change alert - Unforunately, Settings has stopped
I found the issue is because I had disabled the Samsung Account app using CleanMaster's App Manager (which allows me to disable any app including system apps). Once I re-enabled it and updated it, I was able to sign in to my Samsung account and change the settings.

I disabled (saved) and re-enabled (saved again) the SIM change alert feature, after also changing the custom alert message. SMS messages were not sent out anymore.

This also restored Samsung Account as a choice in the Accounts section.