Strictly speaking, a decision by a federal district court—such as Kitzmiller—is only a decision by the lowest-level court: a trial decision. It only binds the parties to that decision. So Judge Jones’ decision does not forbid a school board in Kansas or Kentucky or California from adopting the exact same ID policy that the Kitzmiller decision finds unconstitutional. However, a decision that is so thorough, and so convincing, and so clear, is likely to be extremely persuasive to other federal district judges.
This is especially true given the fact that it relies strongly on McLean, a decision from another District Court. It, too, is technically not binding outside of Arkansas, but McLean is so clear, and strong, that Kitzmiller and other decisions have relied upon it. So, as a practical matter, Kitzmiller is a major victory for science throughout the nation. Should any other school district adopt a similar policy, a parent could go to court with the Kitzmiller decision, and, I think, very quickly get an injunction against that school district as well.
Can Kitzmiller be appealed? Obviously. But this decision is so tight, and so well-grounded in the facts, that I don’t see an appellate court reversing it. Remember that an appeal focuses on legal errors, not on factual errors. So to appeal, the School Board would have to argue that Judge Jones erred in his application of the law. Perhaps they would argue (as they did before Judge Jones) that the Endorsement Test is not appropriate for analyzing whether the ID policy violated the Establishment Clause. It would be extremely unlikely for the Third Circuit to agree with this, however; as Judge Jones’ opinion demonstrates, the Endorsement Test has been repeatedly used by the Third Circuit itself. The School Board might appeal, arguing that the Lemon Test should be abandoned and that Judge Jones was wrong to use it. This, too, would be a very uphill battle for the Board, since the Supreme Court has continually reiterated the validity of the Lemon Test, and the Third Circuit has no power to overrule the Supreme Court. But in any case, to succeed on appeal, the School Board would have to argue that the law was wrongly applied—challenging Jones’ factual findings would be very, very difficult for them, since the Court of Appeals will defer to him on these. And as a matter of law, Kitzmiller is a pretty easy case: just fit the facts into the Lemon Test and see what comes out. Since Kitzmiller, therefore, was primarily about facts, and not primarily about law, it is unlikely that an appeal—should one be forthcoming—would succeed.
And, of course, as commenter Bayesian Bouffant, FCD, reminds us, the decision is also based in large part on the Pennsylvania State Constitution. Although the Court of Appeals would have jurisdiction to consider this issue also on appeal, it adds even more to the burden against the Board if they were to try to appeal this decision.