How does future secrecy fail for Signal group messaging?
Note: It seems that future secrecy fails due to the ability to join a group just by knowing its GroupID.


Correct, this seems to be the issue. Since an attacker can join a group by learning some of the session states and thereafter compromise all messages due to being a part of the group, the group protocol lacks future secrecy.

From the paper (page 8 of the pdf): "After adding herself to the group, the confidentiality of future plaintext messages is compromised."


  Assuming that group update messages are properly authenticated, does future secrecy still fail for Signal's group messaging?


Due to the use of the double ratchet, it would retain that property if knowing the session state would not allow joining the group. But details matter in achieving that. It is not sufficient to just authenticate the group update since we are talking about a situation where the keys of one party are compromised.

However, you are right that it seems to be only the group administration that needs to be fixed.