I have the same problem and have had it for years. I cannot use beta.apple.com to download public profiles. Once in a blue moon I gather the energy to start another round of Apple support with regards to this problem... And every time I get sent from one department to the next... and nobody ever seems to know what the problem is and nobody ever seems to think they should take ownership. So yeah, there's probably thousands of us... in limbo... with their Apple IDs... There is nothing we can do to fix it and the problem does not seem to register as a big enough issue at Apple for them to assign an engineer to figure out what goes wrong in their backend when our Apple IDs sign in to Feedback Assistant or the beta.apple.com website. I am currently in "discussion" with some Apple folk... again... but they keep sending me the same pre-composed emails that I've seen in prior years, so nothing will come of it now either.

You can probably still use it as your Apple ID... but you cannot receive email at it. I am in the same boat. I have a @mac.com but through the .Mac -> MobileMe -> iCloud transition I stopped paying for it and now I can't receive email at it. Which is annoying, because Apple does send App Store invoices to it. (they just never arrive)

It is an email addres. I have an @mac.com Apple ID as well, and me too... cannot receive email at it. It is a domain that is under Apple's control, they have our primary email address... they are just not willing to register the @mac.com Apple IDs as email aliases of the primary email account. Which is strange because they actually send us email to that account. One would think it is in their interest that (App Store) invoices arrive... but no :)

It got solved... I don't know how... but after years of it not working for me, signing up again to the public beta now works again. Yay