I believe I've fixed the HBO Max login problem
So I've been in the same boat as the rest of you that should be getting HBO Max as part of your qualified AT&T Unlimited mobile plan. I'm very familiar with user authentication services/protocols (what I do for a living) and I'm pretty confident that the problem has something to do with how the credentials handshake is happening.
My troubleshooting observations:
I login to my AT&T wireless account with my mobile number and password. When I try to login to AT&T account with the billing address email, it fails because the account doesn't recognize it as a valid user ID.
I'm hypothesizing that binding the HBO Max service to an account seems to require the user ID to be in an email address format since using my mobile number or email address on the account also fails to go through.
Here's what I did that worked (in the order listed):
Login to your AT&T wireless account with my mobile number.
Go to your account profile, sign-in info and change your user ID to an email address format.
Verify the change with the link that will be sent to the email address you decide on.
Log out and log back in to your AT&T account using your new user ID (in email address format).
Go to your account profile, sign-in info and confirm that your user ID is now the email address format.
Click on that blue banner for unlimited customers and follow the text to validate your mobile number process
You should be taken to a page to select HBO Max (heading on the page reads: Big. Streaming. Deal.)
Clicking on the HBO Max button will take you to an AT&T TV Now login page. Use your new user ID in email address format to login using your AT&T wireless account.
Once you go through this, and it took a few page refreshes because AT&T's site performance is atrocious, you'll eventually end up at this site (https://www.att.tv/watchnow) in a logged-in state.
Finally, go to your HBO Max app on your phone and attempt to activate using AT&T as the provider and logging in using the AT&T account with the email address user ID that you set up in steps 2-4.
All of this worked for me and I can't guarantee that it'll work for you, but give it a shot and I hope it solves your problem