A school board is not a monarchy in its realm and during its term. It is subject to the US Constitution and must respect the rights of the citizens. It can be sued for failing to do so.
A few thoughts. You're quite right, a school board is not a monarchy or even an oligarchy...it is subject to the voters. What you're implicity endorsing is a "monarchy", or really, a tyranny of the judiciary. A judge is not a monarch, and yet the judicial branch in recent decades has acted like one...and, like a monarch, a judge cannot be removed except under the most extreme cases...in essence, a judge is a judge for life.
Secondly, the Constitution addresses the prohibition of Congress (not a school board or a state) passing a religious law. So, even though the judge used the Constitution as an excuse to insert his curriculum preferences into the town's schools, such an argument is not germane.
As for being sued, anyone can be sued for anything.
I am appalled that a federal judge is deciding curriculum. The people of the city or school district have that job. Nowhere does the Constitution give the federal government ANY right to decide what local schools teach.