Sorry to resurrect this thread, but I believe I've encountered another problem. I was able to turn off Advanced Data Protection, but I still encountered problems with my older devices - so I think my post above about 2FA not causing the problem is wrong. I was later trying to turn off 2FA and came across this (Two-factor authentication for Apple ID - Apple Support) which contains this gem:
If you're already using two-factor authentication with your Apple ID, you can't turn it off. If you updated to two-factor authentication inadvertently, you can turn it off within two weeks of enrollment. If you do, your account is less secure and you can't use features that require a higher level of security.
Now I not only can't use my 2017 MBA, I believe I'm encountering problems with using AppleTV on my big screen TVs. If anyone can confirm that, it would at least stop me from flailing about trying to figure out the issue. (Note - AppleTV on my Samsung had kicked me out the other day, but I was given a QR code that I could scan and use with my iPhone to login. Now I'm not given that option, or anything like "use your phone to login" - and when I manually type in my AppleID and PW, I just get an error message.)