I tried
https://www.lds.org/ and "lo and behold" there was NO security warning message. Thanks for that suggestion!
Both sites are in the Internet Zone.
Now I know how to by-pass the warning message, even if i don't know why it shows up.
But it's a fine starting point, and maybe I'll figure it out over time.
All right!
I found out the cause very quickly after using +BudMan's idea.
The culprit was Ad Muncher (popup etc. blocker). So, somewhere in it's default filters there must be a reference to the LDS website.
Thanks everyone for addressing my problem.
I just added "minimal filtering" into the Custom Filters box, and problem solved.