Solution which worked for me:

  1. Open Music app
  2. Sign-in with Apple ID
  3. Accept agreement which would not initiate in appstore.
  4. Open AppStore & sign in with same Apple ID.

It may be late but could be useful for someone else.

So, I just faced the same issue where I was being asked to Review the iTunes account in a loop.

The solution is to open your AppStore > click on your Profile Icon from the top right corner > and complete the review process there.