As somebody whose dad was involved in getting 2 schools built while I was in school and was also president of the schoolboard for a time before that, I can confidently say that anybody who runs for a schoolboard position is doing so because they have an agenda.
Oftentimes, that agenda is "I want our schools to be better for our kids," but not always. Sometimes, people run because they have differing opinions on what making schools better means, but sometimes (and rather often right now, it seems) you get somebody whose only goal is to burn it to the ground. Those are the kinds of people who care about political parties in schoolboards - because they're so obsessed with the us vs. them of their politics that it shapes the rest of their lives.
Local politics can be a cutthroat and dirty game. I'll always remember my dad telling me about how he was walking out of a town meeting one time when he saw an old lady point to him and loudly say to her friends, "That's him! That's the enemy!"