I don't understand the cryptosystems in play enough to say what's possible. I understand ABE only at a very high level, and haven't yet seen a cryptosystem which boasts ABE.

As to certifying certain users with certain attributes in a privacy-preserving fashion, that's trivial. Alice wants to be certified as a female resident of Alaska by Public Records 'r' Us (PRU). PRU encrypts each of Alice's attributes (female, Alaska resident) with different symmetric keys, and encrypts all of the attribute ciphertexts together with Alice's account name/ID with a final ID symmetric key, and sends Alice the ID and attribute keys. Alice can prove to Bob that she is identified by providing him the ID key, and she can prove certain attributes by providing their respective keys in addition. Eve is unable to discern any relationship between Alice and PRU, or between Alice and Bob, and is also ignorant to Alice's attributes. Bob only knows the attributes about Alice that she gives him keys for. PRU can revoke any attribute at any time by updating the blockchain object.

The biggest issue I see with that system is that once Alice reveals attributes to Bob, Bob can reveal them to others. I don't know of a way to combat this off the top of my head.