As the state's attestation requirements for mailed-in votes is only imposed in a few states, and the state has not advanced any interest behind it, lower court's entry of consent judgement abrogating the requirement should not be stayed. The elevated standard for stays close to an election is met, as the last election didn't have the requirement, and the state hasn't suggested that it would confuse voters. Political party has standing to intervene for the purposes of the pending appeal.
Since 2011. An occasional commonplacing of the U.S. Circuit Courts of Appeal.
Neither an authoritative statement of the law nor legal advice. Quick work.