You're right that the party of the president that appointed a judge is not a perfect predictor of how they will rule in any of the NWS cases.
However, in this particular case, we have already seen how the same judges who will hear the appeal (presumably the entire Fifth Circuit en banc) voted on the APA and constitutional claims the first time around.
Saying that any judge appointed by a Republican president will vote for us and any judge appointed by a Democratic president will vote against is oversimplification. But that already happened in this very case in the Fifth Circuit, so it is reasonable to expect it to happen again.