Thank you for your reply. I was not aware that @Mac.com was an alias to @iCloud.com. If aliasing is the issue, next question of course becomes: Why does @Mac.com not work but @me.com does? Both appear to be aliases to @iCloud.com. I realize this is a little "inside baseball" but the article you referenced is dated 2016 and @Mac.com worked as a login until only a few weeks ago. I am confident of this date (2/26/21) because when this happened I changed my password, believing that my password record had become corrupted, and. my password manager records the date of all changes/updates.
Finally I note that both my Mac and my phone are logged into iCloud services (photos, mail, contacts, calendars, reminders, etc) for syncing purposes using the @mac.com address and password and the sync works fine. (I confirmed this by looking at the account name in System Preferences/Internet Accounts on Big Sur, and Settings/AppleID on the phone.) If I can't log into iCloud using a @Mac.com address, I would think this sync would not work.
Please note that I am using the same password for @Mac.com, @me.com, and @iCloud.com. This tells me that the password is not the problem.
Again, this is confusing and I'm not sure we are at the bottom of the problem yet. Simply stated: I can (and am) logged into iCloud services (including mail, contacts, photos sync, 200GB storage, etc) as well as purchasing items on iTunes and AppleTV using the @Mac.com address. But a select few services (Apple discussions, appleid.apple.com, and maybe a few others) require the @me.com address. Hopefully we can get to the bottom of this.
