I contacted technical support. They gave the usual - Try it, you'll like it approach. They wanted me to uninstall/reinstall Office on my MAC.
Note that it is never necessary to do anything that drastic on a Mac.
I asked them to add an option to say NO (no I do not want to share data) and they just said they will make a note of the problem.
When I update my MacOS, sometimes there is a pop-up asking me if I want to share data. There is always an option to say no. I am asked the question once and then I never see that question again.
So it looks like I either have to leave Word and Excel open all the time or just have to close that annoying pop up every time I open Word and Excel.
Thanks for trying to find a solution.