Huh? How does a judge "not allow someone to appeal"?
Twitter and the NYCLU are alleging that by holding Twitter in contempt for not honoring a court order, the judge is effectively infringing on their right to appeal. That's a sane argument, but it isn't the same thing as "not allowing them to appeal". Moreover, if there was a clear and urgent grounds for appeal, the appeals court could expedite the challenge. They haven't.
Twitter and the NYCLU are alleging that by holding Twitter in contempt for not honoring a court order, the judge is effectively infringing on their right to appeal. That's a sane argument, but it isn't the same thing as "not allowing them to appeal". Moreover, if there was a clear and urgent grounds for appeal, the appeals court could expedite the challenge. They haven't.