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Hi Tereza,
Thank you so very much for your assistance. It turns out that there was a problem with my new phone which resulted in my having to do a factory reset. When I re-transferred all my data from my old phone, whatever was causing that message was cleared up, and I wasn’t prompted for a password when I tried to turn on the Chrome protection setting.
All is well now. 
Again, many thanks for all of your help.
Best regards,
mybuddy1998